Seminar on algebraic cobordism

Meeting time and place:

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

Program

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

 

Schedule

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.

Bibliography

[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.

 

Archiv

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