Motives with modulus

Principal Investigators

Prof. Dr. H. Esnault (FU Berlin)
Prof. Dr. M. Kerz (Regensburg)
Prof. Dr. M. Levine (Essen)

Scientific Staff

Tom Bachmann (Essen-01.04.2016-30.09.2018)
Wataru Shimura (Essen-30.08.2016-30.03.2017)
Federico Binda (Essen-01.10.2015-30.08.2016)
Fabio Tonini (Berlin-01.10.2015-30.09.2018.)

Project description

Our aim is to construct a refinement of the triangulated category of mixed motives of Voevodsky, yielding a theory with modulus, or what is essentially the same, a theory which involves schemes with non-reduced structure. This expected refined motivic category should be a rigid tensor triangulated category having Voevodsky’s category as a Verdier quotient category.

Related publications

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.