Seminar on algebraic cobordism

Meeting time and place:

We meet on Tuesdays,16-18 Uhr (c.t.), in WSC-S-U-3.05


This semester we will hold a seminar on algebraic cobordism from the point of view of motivic homotopy theory and algebraic geometry.



Lecture 1. 19.4. Gabriela Guzman. A review of SH(S) and the construction of MGL: a description of symmetric T-spectra with motivic model structure and a construction of MGL as a symmetric monoid in symmetric T-spectra, see for example [H], [J] and [PPR].

Lecture 2. 26.4./3.5 Maria Yakerson. Universality of MGL-following the paper of Panin-Pimenov-Roendigs [PPR].

Lecture 3. 10.5./17.5 Lorenzo Mantovani. Steenrod operations from Voevodsky’s paper [V]. Mainly we need the structure theorem for H(Z/p)∧H(Z/p) for p prime to the characteristic

Lecture 4. 31.5. Aurélien Rodriguez. Brown representability and Landweber exactness-following the papers of Naumann-Spitzweck [NS] and Naumann-Spitzweck-Ostvar [NSO].

Lecture 5. 7.6. Adeel Khan. MGL and HZ I: the paper of Hoyois [Ho] proving the Hopkins-Morel theorem, part 1.

Lecture 6. 14.6 Andre Chatzistamatiou. MGL and HZ II: the paper of Hoyois [Ho] proving the Hopkins-Morel theorem, part 2.

Lecture 7. 20.6. (Note special Monday meeting) Elden Elmanto. Slices of Landweber exact theories and Atiyah-Hirzebruch spectral sequences-Spitzweck’s paper [S].

Lecture 8. 28.6. Vladimir Sosnilo. Geometric algebraic cobordism: an overview of Levine-Morel algebraic cobordism, the construction, main properties, degree formulas. from [AC]

Lecture 9. 5.7. Federico Binda. Double point cobordism-The paper of Levine-Pandharipande [LP], applications to D-T theory.

Lecture 10.12.7. Toan Nguyen. Ω*=MGL2*,* and generalisations. This is from [L2] and [LT].

Lecture 11. 19.7. ?

For the last lecture, we’ll have to see. We could give additional applications to D-T theory, or look at the equivariant case with applications to geometric representation theory. Or talk about other “unoriented” theories like MSL, MSp. Or you can make other suggestions, just let me know.


[H] Hovey, M., Spectra and symmetric spectra in general model categories. J. Pure Appl. Algebra 165(2001), no. 1, 63-127.

[Ho] Hoyois, M. From algebraic cobordism to motivic cohomology. J. Reine Angew. Math. 702 (2015), 173–226.

[J] Jardine, J.F., Motivic symmetric spectra. Doc. Math. 5(2000) 445-553.

[L] Levine, M. Comparison of cobordism theories. J. Algebra 322(2009), no. 9, 3291–3317.

[LM] Levine, M.; Morel, F. Algebraic cobordism. Springer Monographs in Mathematics. Springer, Berlin, 2007. xii+244 pp.

[LP] Levine, M.; Pandharipande, R. Algebraic cobordism revisited. Invent. Math. 176 (2009), no. 1, 63–130.

[LT] Levine, M.; Tripathi, G. S., Quotients of MGL, their slices and their geometric parts. Doc. Math. 2015, Extra vol.: Alexander S. Merkurjev's sixtieth birthday, 407–442.

[NS] Naumann, N.; Spitzweck, M., Brown representability in A1-homotopy theory. J. K-Theory 7(2011), no. 3, 527–539.

[NSO] Naumann, N., Spitzweck, M., Ostvar, P.A., Motivic Landweber exactness. Doc. Math. 14(2009), 551–593.

[PPR] Panin, I., Pimenov, K. and Röndigs, O., A universality theorem for Voevodsky's algebraic cobordism spectrum. Homology, Homotopy Appl. 10(2008), no. 2, 211–226.

[S] Spitzweck, M., Slices of motivic Landweber spectra. J. K-Theory 9(2012), no. 1, 103–117.

[V] Voevodsky, V., Motivic Eilenberg-MacLane spaces. Publ. Math. Inst. Hautes Études Sci. 112(2010) 1–99.



Motives-WS 2015/16

Motives-SS 2015

Motives-WS 2014/15

There was no motives seminar SS 2014 due to the Special Semester in Motivic Homotopy Theory

Motives-WS 2013/14

Motives-SS 2013

Motives-WS 2012/13

Motives-SS 2012

Motives-WS 2011/12