Mixed Hodge structures in homotopy theory

J. J. Cirici, D. Egas Santander, M. Livernet and S. Whitehouse, Derived A-infinity algebras and their homotopies. Topology and its Applications, 235, 214--268 (2018). (also available at http://arxiv.org/abs/1609.08077).

D.Chataur, J.Cirici, Rational homotopy of complex projective varieties with normal isolated singularities. Forum Mathematicum 29 (2017), no.1, 41--57 

J.Cirici, F. Guillén, Homotopy theory of mixed Hodge complexes.Tohoku Mathematical Journal 68 (2016), no.3, 349--375.

J. Cirici, Cofibrant models of diagrams: mixed Hodge structures in rational homotopy.  Transactions of the American Mathematical Society 367 (2015), no.8, 5935--5970.

U. Buijs and F. Cantero and J. Cirici, Weight decompositions of Thom spaces of vector bundles in rational homotopy theory.Journal of Homotopy and Related Structures, 15, 1--26 (2020).

J. Cirici and G. Horel, Mixed Hodge structures and formality of symmetric monoidal functors. Annales Scientifiques de l'École Normale Supérieure, 53(4):1071--1104 (2020).

J. Cirici and A. Roig, Sullivan minimal models of operad algebras. Publicacions Matemàtiques, 63, no 1, 125--154 (2019).

D. Chataur and J. Cirici, Rational Homotopy and Intersection-Formality of Complex Algebraic Varieties. Revista Matemàtica Complutense, 31, no 2, 479--524 (2018).

D. Chataur and J. Cirici, Mixed Hodge structures on the intersection homotopy type of complex varieties with isolated singularities. arXiv:1603.09125 [math.AT] 2016

Motivic stack inertia for modui spaces of curves, variation of periods and multiple zeta values in genus 0 and 1.

B. Collas, S. Maugeais, Hurwitz Stacks of Groups Extensions and Irreducibility. arxiv:1803.06212.

B. Collas, M. Dettweiler, S. Reiter, Monodromy of elliptic curve convolution and $G_2$-motives of Beauville-Katz type arXiv:1803.05883

B. Collas, S. Maugeais, On Galois action on stack inertia of moduli spaces of curves. arXiv:1412.4644.

Motivic iterated integrals and integral points

Ishai Dan-Cohen, and Stefan Wewers, Mixed Tate motives and the unit equation. International Mathematics Research Notices, Issue 17, 2016

Ishai Dan-Cohen and Tomer Schlank, Morphisms of rational motivic homotopy types. Appl. Categ. Structures 29 (2021), no. 2, 311–347

Preprints

Ishai Dan-Cohen, Explicit motivic Chabauty-Kim theory III: towards the polylogarithmic quotient over general number fields. 28 pages. arxiv.org/abs/1510.01362

Ishai Dan-Cohen, Rational motivic path spaces and Kim's relative unipotent section conjecture, arXiv:1703.10776 To appear, Rendiconti del Seminario Matematico della Università di Padova.

Motives with modulus

Tom Bachmann, Motivic and Real Etale Stable Homotopy Theory. Compos. Math. 154 (2018), no. 5, 883–917.

Tom Bachmann, The Generalized Slices of Hermitian K-Theory. K-theory. J. Topol. 10 (2017), no. 4, 1124–1144.

Tom Bachmann, Some Remarks on Units in Grothendieck-Witt Rings. J. Algebra 499 (2018), 229–271.

Tom Bachmann and Alexander Vishik, Motivic equivalence of affine quadrics. Math. Ann. 371 (2018), no. 1-2, 741–751.

Tom Bachmann and Jean Fasel, On the effectivity of spectra representing motivic cohomology theories. https://arxiv.org/abs/1710.00594.

Hélène Esnault, Michael Harris, Chern classes of automorphic vector bundles, Pure and Applied Mathematics Quarterly 13 (2) (2017), 193--213.

H. Esnault, M. Kerz and O. Wittenberg, A restriction isomorphism for cycles of relative dimension zero. Cambridge Journal of Mathematics 4 2 (2016), 163--196.

Fabio Tonini and Lei Zhang. Algebraic and Nori Fundamental Gerbes. Journal of the Institute of Mathematics of Jussieu , pages 1-43, jul 2017.

Fabio Tonini and Lei Zhang. F -divided sheaves trivialized by dominant maps are essentially finite.  Transactions of the American Mathematical Society, 371 (2019)

M. Kerz, Y. Zhao, Higher ideles and class field theory. Nagoya Math. J. 236 (2019), 214–250.

M. Kerz, S. Saito, >Chow group of 0-cycles with modulus and higher-dimensional class field theory. Duke Math. J. 165 (2016), no. 15, 2811–2897.

M. Kerz, Transfinite limits in topos theory, Theory Appl. Categ. 31 (2016), Paper No. 7, 175–200.

Wataru Kai and H. Miyazaki, Suslin's moving lemma with modulus. Annals of K-theory 3 (1) 2018, 55-70.

Wataru Kai and Ryomei Iwasa, Chern classes with modulus. Nagoya Math. J. 236 (2019), 84–133.

F.Binda and S.Saito, Relative Cycles with moduli and regulator maps,J. Inst. Math. Jussieu, 18 (2019), pp. 1233–1293.

F.Binda, J.Cao, W.Kai, R.Sugiyama, Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus,J. Algebra, 469 (2017), pp. 437–463.

F.Binda and A.Krishna, Zero cycles with modulus and zero-cycles on singular varieties Compos. Math., 154 (2018), pp. 120–187.

F.Binda Torsion zero-cycles with modulus on affine varieties J. Pure Appl. Algebra, 222 (2018), pp. 61–74.

F.Binda A cycle class map for 0-cycles with modulus to higher relative K-groups Doc. Math., 23 (2018), pp. 407–444.

Characterizations and uniqueness of the stable motivic homotopy category

F. Beckert and M. Groth, Abstract cubical homotopy theory arXiv:1803.06022.

J. Hornbostel, Some comments on motivic nilpotence (with an appendix by M. Zibrowius). Transactions of the AMS 370 (2018), 3001-3015

J. Hornbostel, M. Wendt, Chow-Witt rings of classifying spaces for symplectic and special linear groups, J. Topol. 12 (2019), no. 3, 916–966.

Motivic invariants of moduli spaces

A. Schmitt, A remark on relative geometric invariant theory for quasi-projective varieties. Math. Nachr. 292 (2019), no. 2, 428–435.

Ángel Luis Muñoz Castañeda, A. Schmitt,, Singular principal bundles on reducible nodal curves. arxiv1911.01578 To appear: Trans. Amer. Math. Soc.

A.Schmitt, A general notion of coherent systems, hal-02391836

V. Hoskins, Victoria, S. Pepin Lehalleur, A formula for the Voevodsky motive of the moduli stack of vector bundles on a curve. Geom. Topol. 25 (2021), no. 7, 3555–3589.

V. Hoskins, Victoria, S. Pepin Lehalleur, On the Voevodsky motive of the moduli stack of vector bundles on a curve. Q. J. Math. 72 (2021), no. 1-2, 71–114.

Applications of motivic methods to differential forms and birational geometry

Shane Kelly, Voevodsky motives and ldh descent. Astérisque 391 (2017).

Annette Huber, Differential forms in algebraic geometry -- a new perspective in the singular case. Portugaliae Mathematica 73 (2016), no. 4, 337--367.

Ofer Gabber, Shane Kelly, Points in algebraic geometry. J. Pure Appl. Algebra 219 (2015), no. 10, 4667–4680.

Annette Huber, Shane Kelly, Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces .Algebra Number Theory 12 (2018), no. 3, 649–692.

Annette Huber, Stefan Kebekus, Shane Kelly, Differential forms in positive characteristic avoiding resolution of singularities. Bull. Soc. Math. France 145 (2017), no. 2, 305–343.

Shane Kelly, Un isomorphisme de Suslin. Bull. Soc. Math. France 146 (2018), no. 4, 633–647.

Shane Kelly, Shuji Saito, Weight homology of motives. Int. Math. Res. Not. IMRN 2017, no. 13, 3938–3984.

Shane Kelly, Some observations about motivic tensor triangulated geometry over a finite field. ``Bousfield classes and Ohkawa's theorem'', 221–243, Springer Proc. Math. Stat., 309, Springer, Singapore, [2020], ©2020.

Jens Niklas Eberhardt, Shane Kelly, Mixed Motives and Geometric Representation Theory in Equal Characteristic. Selecta Math. (N.S.) 25 (2019), no. 2, Paper No. 30, 54 pp.

The Summand $BtmfP$ of $MU\langle 6\rangle$

Laures, G. and Olbermann, M..Cannibalistic classes of string bundles. Manuscripta Math. 156 (2018), no. 3-4, 273–298.

Laures, G. and Schuster, B.  Towards a splitting of the K(2)-local string bordism spectrum, Proc. Amer. Math. Soc. 147 (2019), no. 1, 399–410.

Gerd Laures, Characteristic classes in $TMF$ of level $\Gamma_1(3)$, Trans. Amer. Math. Soc. 368 (2016), no. 10, 7339--7357.

Gerd Laures and Martin Olbermann, $TMF_0(3)$-characteristic classes for string bundles, Math. Z. 282 (2016), no. 1-2, 511--533.

Nils Schulenberg, Indecomposable Summands in Real and Complex Thom Spectra (thesis 2019) docId/6555

Expansion principles for topological automorphic forms

Hanno von Bodecker, Sebastian Thyssen. Topological Automorphic Forms via Curves  arXiv:1705.02134.

Hanno von Bodecker and Sebastian Thyssen, On p-local Topological Automorphic Forms for $U(1,1;\mathbb{Z}[i])$. arXiv:1609.08869, 2016

Motivic filtrations over Dedekind domains

Ananyevskiy, Alexey, Levine, Marc, Panin, Ivan. Witt sheaves and the $\eta$-inverted sphere spectrum. J. Topol. 10 (2017), no. 2, 370--385.

Fangzhou Jin, Enlin Yang, Künneth formulas for motives and additivity of traces. Adv. Math. 376 (2021), Paper No. 107446, 83 pp.

Frédéric Déglise, Fangzhou Jin, Adeel A. Khan, Fundamental classes in motivic homotopy theory. J. Eur. Math. Soc. (JEMS) 23 (2021), no. 12, 3935–3993.

Marc Levine, An overview of motivic homotopy theory. Acta Math. Vietnam. 41 (2016), no. 3, 379–407.

Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, Cellularity of hermitian K-theory and Witt theory ``K-Theory—Proceedings of the International Colloquium, Mumbai, 2016'', 35–40, Hindustan Book Agency, New Delhi, 2018.

Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, The motivic Hopf map solves the homotopy limit problem for K-theory Doc. Math. 23 (2018), 1405–1424.

Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær, The first stable homotopy groups of motivic spheres, Ann. of Math. (2) 189 (2019), no. 1, 1–74.

J.D. Christensen, M. Frankland, Higher Toda brackets and the Adams spectral sequence in trianglated categories, Algebr. Geom. Topol. 17 (2017), no. 5, 2687–2735.

H.J. Baues, M. Frankland, Eilenberg-MacLane mapping algebras and higher distributivity up to homotopy, New York J. Math. 23 (2017), 1539–1580.

Frédéric Déglise, Jean Fasel, Fangzhou Jin, Adeel A. Khan, On the rational motivic homotopy category, arXiv:2005.10147. Preprint 2020. To appear, Journal de l'École polytechnique

Fangzhou Jin, Heng Xie A Gersten complex on real schemes Preprint 2020. arXiv:2007.04625.

Lorenzo Mantovani, Localizations and completions in motivic homotopy theory. arXiv:1810.04134. Preprint October 2018

M. Frankland, A user's guide: Completed power operations for Morava E-theory, expository article at mathusersguides.org, 2016.

M. Frankland, M. Spitzweck, A possible approach to the Hopkins-Morel isomorphism over general base schemes, Work in progress.

Chromatic derived algebraic geometry and equivariant homotopy theory

Ben Antieau and Lennart Meier. The Brauer group of the moduli stack of elliptic curves. Algebra & Number Theory, Vol. 14 (2020), No. 9, 2295–2333 arXiv:1608.00851

Lennart Meier and Viktoriya Ozornova. Rings of modular forms and a splitting of \(TMF_0(7)\), Selecta Mathematica (2020) 26:7

Rosona Eldred, Gijs Heuts, Akhil Mathew and Lennart Meier. Monadicity of the Bousfield-Kuhn functor. Proc. Amer. Math. Soc. 147 (2019), 1789-1796 arXiv:1707.05986

Mike Hill and Lennart Meier. The \(C_2\)-spectrum \(Tmf_1(3)\) and its invertible modules Algebraic & Geometric Topology 17 (2017) 1953-2011.

Preprints

Lennart Meier. Decomposition results for rings of modular forms. arXiv:1710.03461

Lennart Meier. Topological modular forms with level structures: decompositions and duality. arXiv:1806.06709

Beyond spin bordism

Akhil Mathew, Niko Naumann and Justin Noel, Nilpotence and descent in equivariant stable homotopy theory. Advances in Mathematics, vol.\ 305, pp.\ 994-1084, January 2017.

Tobias Barthel, Markus Hausmann, Niko Naumann and Justin Noel, Thomas Nikolaus, and Nathaniel Stapleton The Balmer spectrum of the equivariant homotopy category of a finite abelian group. Invent. Math. 216 (2019), no. 1, 215–240.

Akhil Mathew, Niko Naumann and Justin Noel, Derived induction and restriction theory. Geom. Topol. 23 (2019), no. 2, 541–636

Dustin Clausen, Akhil Mathew, Niko Naumann and Justin Noel, Descent in algebraic $K$-theory and a conjecture of Ausoni-Rognes. J. Eur. Math. Soc. (JEMS) 22 (2020), no. 4, 1149–1200.

New examples of logarithmic ring spectra

Birgit Richter, Brooke Shipley, An algebraic model for commutative H$\mathbb{Z}$-algebras, Algebr. Geom. Topol. 17 (2017), no. 4, 2013--2038.

Irina Bobkova, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter, Inna Zakharevich, On the higher topological Hochschild homology of $\mathbb{F}_p$ and commutative $\mathbb{F}_p$-group algebras, in: Women in Topology: Collaborations in Homotopy Theory. Contemporary Mathematics 641, AMS, 2015, 97--122.

Birgit Richter, On the homology and homotopy of commutative shuffle algebras, Israel Journal of Mathematics 209 (2), 2015, 651--682.

John Rognes, Steffen Sagave, and Christian Schlichtkrull, Localization sequences for logarithmic topological Hochschild homology, Mathematische Annalen, 363 (2015), no. 3, 1349–1398

Birgit Richter, Steffen Sagave. A strictly commutative model for the cochain algebra of a space. Compos. Math. 156 (2020), no. 8, 1718--1743.

Gemma Halliwell, Eva Höning, Ayelet Lindenstrauss, Birgit Richter, Inna Zakharevich, Relative Loday constructions and applications to higher THH-calculations, Topology and its Applications 235 (2018), 523--545.

Bjørn Ian Dundas, Ayelet Lindenstrauss, Birgit Richter, On higher topological Hochschild homology of rings of integers, Math. Research Letters 25, 2 (2018), 489--507.

John Rognes, Steffen Sagave, and Christian Schlichtkrull, Logarithmic topological Hochschild homology of topological K-theory spectra, J. Eur. Math. Soc. (JEMS) 20 (2018), no. 2, 489--527.

Bjørn Ian Dundas, Ayelet Lindenstrauss, Birgit Richter, Towards an understanding of ramified extensions of structured ring spectra, Mathematical Proceedings of the Cambridge Philosophical Society 168 (3) (2020), 435--454.

Birgit Richter, Commutative ring spectra arXiv:1710.02328 to appear in: Stable categories and structured ring spectra, edited by Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill, MSRI Book Series, Cambridge University Press.

Operadic structures in motivic homotopy theory

A.Ananyevskiy, O.Röndigs, P.A. Østvær. On very effective hermitian \(K\)-theory. Math. Z., 294(3-4):1021--1034, 2019.

O. Röndigs, M. Spitzweck und P.A. Østvær. The motivic Hopf map solves the homotopy limit problem for \(K\)-theory. Doc. Math. 23 (2018), 1405-1424.

O. Röndigs,On the \(\eta\)-inverted sphere. In ``\(K\)-Theory, volume 19 of Tata Inst. Fundam. Res. Stud. Math.'', 41--63. Tata Inst. Fund. Res., Mumbai, 2018.

O. Röndigs, M. Spitzweck, P.A. Østvær. Cellularity of hermitian K-theory and Witt-theory. In ``\(K\)-Theory, volume 19 of Tata Inst. Fundam. Res. Stud. Math.'', 35--40. Tata Inst. Fund. Res., Mumbai, 2018.

Kyle Ormsby, Oliver Röndigs, Paul Arne Østvær, Vanishing in stable motivic homotopy sheaves Forum Math. Sigma 6 (2018), Paper No. e3, 20 pp.

G. Biedermann, G. Raptis, M. Stelzer, The realization space of an unstable coalgebra, Astérisque No. 393 (2017), viii+148 pp.

H. Heine, M. Spitzweck, A. Lopez-Avila. Infinity categories with duality and hermitian multiplicative infinite loop space machines. Preprint (submitted), arXiv:1610.10043

M. Frankland, M. Spitzweck. Towards the dual motivic Steenrod algebra in positive characteristic. Preprint 2017, arXiv:1711.05230

M. Spitzweck. A Grothendieck-Witt space for stable infinity categories with duality. arXiv:1610.10044

M. Stelzer, Simplicial coalgebras over a Prüfer domain and homotopy theory. Preprint

Classification of vector bundles over affine varieties.

Tariq Syed, A generalized Vaserstein symbol Annals of K-Theory 4 (2019), no. 4, 671-706

Tariq Syed, The cancellation of projective modules of rank 2 with a trivial determinant, Algebra & Number Theory 15 (2021), no. 1, 109-140

Tariq Syed, Cancellation of vector bundles of rank 3 with trivial Chern classes on smooth affine fourfolds, Preprint (2020) to appear in JPAA arxiv 2010.07690

Tariq Syed, Symplectic orbits of unimodular rows, Preprint (2020) arxiv 2010.06669

Global equivariant homotopy theory
Global equivariant homotopy theory, II

Stefan Schwede, Global homotopy theory New Mathematical Monographs 34. Cambridge University Press, Cambridge, 2018. xvi+828 pp. www.cambridge.org/9781108425810.

Christian Wimmer, Rational extensions of the representation ring global functor and a splitting of global equivariant $K$-theory, Bulletin of the London Mathematical Society 50 (2018), 863-873 doi.org/10.1112/blms.12189

Markus Hausmann, Symmetric products and subgroup lattices, Geometry & Topology 22 (2018), no. 3, 1547–1591.

Stefan Schwede, Equivariant properties of symmetric products, Journal of the American Mathematical Society 30 (2017), 673-711.

Stefan Schwede, Orbispaces, orthogonal spaces, and the universal compact Lie group, Mathematische Zeitschrift 294 (2020), 71-107 doi.org/10.1007/s00209-019-02265-1

Markus Hausmann, Symmetric spectra model global homotopy theory of finite groups, Algebr. Geom. Topol. 19 (2019), no. 3, 1413–1452. doi.org/10.2140/agt.2019.19.1413

Stefan Schwede, Categories and orbispaces, Algebraic & Geometric Topology 19 (2019), 3171-3215 doi.org/10.2140/agt.2019.19.3171

Christian Wimmer, Rational global homotopy theory and geometric fixed points. PhD thesis, Universität Bonn, 2017

Markus Hausmann, Dominik Ostermayr, Filtrations of global equivariant K-theory, Mathematische Zeitschrift 295 (2020), 161--210 doi.org/10.1007/s00209-019-02338-1

Stefan Schwede, Global algebraic K-theory, Journal of Topology 15 (2022), 1325-1454 DOI: 10.1112/topo.12241

Stefan Schwede, Global stable splittings of Stiefel manifolds, Documenta Mathematica 27 (2022), 789-845 DOI: 10.25537/dm.2022v27.789-845

Stefan Schwede, Splittings of global Mackey functors and regularity of equivariant Euler classes, Proceedings of the London Mathematical Society 125 (2022), 258-276 DOI: 10.1112/plms.12446

Preprints

Michael Stahlhauer, \(G_\infty\)-ring spectra and Moore spectra for \(\beta\)-rings. To appear, Algebraic & Geometric Topology. arXiv:2007.14304

Christian Wimmer, Rational global homotopy theory and geometric fixed points. PhD thesis, Universität Bonn, 2017

Sil Linskens, Denis Nardin, Luca Pol, Global homotopy theory via partially lax limits arXiv:2206.01556.

Odd primary equivariant rigidity and equivariant derivators

Irakli Patchkoria, Rigidity in Equivariant Stable Homotopy Theory, Algebr. Geom. Topol. 16 (2016), no. 4, 2159–2227.

Irakli Patchkoria, Constanze Roitzheim, Rigidity and exotic models for $v_1$-local $G$-equivariant stable homotopy theory, Math. Z. 295 (2020), no. 1-2, 839--875.

Irakli Patchkoria, On exotic equivalences and a theorem of Franke, Bulletin of the London Mathematical Society 49 (2017), 1085--1099

Oriented cohomology theories and equivariant motives

V. Petrov, N. Semenov, Rost motives, affine varieties, and classifying spaces, Journal of London Math. Soc. 95 (2017), issue 3, 895-918.

A. Neshitov, V. Petrov, N. Semenov, K. Zainoulline, Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras, Advances in Math. 340 (2018), 791-818.

M. Borovoi, N. Semenov, M. Zhykhovich, Hasse principle for Rost motives, Int. Math. Res. Not., https://doi.org/10.1093/imrn/rny300

P. Sechin, N. Semenov, Applications of the Morava K-theory to algebraic groups, Ann. Sci. Éc. Norm. Supér. (4) 54 (2021), no. 4, 945–990.

V. Petrov, N. Semenov, Hopf-theoretic approach to motives twisted flag varieties, Compos. Math. 157 (2021), no. 5, 963–996.

A. Lavrenov, V. Petrov, P. Sechin, N. Semenov, Morava K-theory of orthogonal groups and motives of projective quadrics, arxiv: 2011.14720 (2020).

Trace maps for real algebraic K-Theory

Emanuele Dotto, Kristian Moi, Irakli Patchkoria Witt Vectors, Polynomial Maps, and Real Topological Hochschild Homology Arxiv:1901.02195 to appear les Annales scientifiques de l'école normale supérieure

Emanuele Dotto, Baptiste Calmès, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, Wolfgang Steimle, Hermitian K-theory for stable infinity-categories I: Foundations arxiv 2009.07223. Preprint 2020.To appear, Selecta Mathematica

Emanuele Dotto, Baptiste Calmès, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, Wolfgang Steimle, Hermitian K-theory for stable infinity-categories II: Cobordism categories and additivity. arxiv 2009.07224 (Preprint 2020).

Emanuele Dotto, Baptiste Calmès, Yonatan Harpaz, Fabian Hebestreit, Markus Land, Kristian Moi, Denis Nardin, Thomas Nikolaus, Wolfgang Steimle, Hermitian K-theory for stable infinity-categories III: Grothendieck-Witt groups of rings. arxiv 2009.07225 (Preprint 2020).

Emanuele Dotto, Achim Krause, Thomas Nikolaus and Irakli Patchkoria, Witt vectors with coefficients and characteristic polynomials over non-commutative rings arxiv 2002.01538 (Preprint 2020) To appear in Compositio Mathematica.

Applications of motivic filtrations

Alexander D. Rahm, Bui Anh Tuan, Matthias Wendt. The Farrell-Tate and Bredon homology for \(PSL_4(\mathbb{Z})\) via rigid facets subdivision. J. Pure Appl. Alg. 223 (7), 2019, pp. 2872-2888, arXiv:1611.06099v2.

Matthias Wendt. Variations in \(\mathbb{A}^1\) on a theme of Mohan Kumar. arXiv:1704.00141v1, (to appear in Int. Math. Res. Not. IMRN

Aravind Asok, Marc Hoyois und Matthias Wendt. Generically split octonion algebras and \(\mathbb{A}^1\)-homotopy theory. Algebra Number Theory 13 (3), 2019, pp. 695-747, arXiv:1704.03657v1.