WiSe 21/22 Oberseminar: Derived algebraic cobordism

Time and place: Tuesday 14:15-15:45 in M311 and online


Algebraic cobordism is a generalized cohomology theory for algebraic varieties originally introduced by V. Voevodsky, which is in many ways analogous to complex cobordism in topology. In particular, the special role of complex cobordism in chromatic homotopy theory was a key inspiration for Voevodsky's celebrated proof of the Bloch–Kato conjecture.

In this seminar, we aim to study a new “elementary” construction of algebraic cobordism, due to T. Annala, which uses derived algebraic geometry and is well-behaved over fields of positive characteristic (unlike the previous construction of M. Levine and F. Morel, which strongly relied on resolution of singularities). In addition to general properties such as the bivariant functoriality and the relationship to algebraic K-theory and Chow groups, we will prove the algebraic Spivak theorem stating that the derived cobordism groups of a perfect field are generated, up to inverting the characteristic, by cobordism classes of smooth varietes.

Date Speaker Topic
26.10 Denis Nardin Derived rings and schemes
02.11 Charanya Ravi Quasi-projective derived schemes
09.11 Luca Pol The cotangent complex, smoothness, and quasi-smoothness
16.11 Jeroen Hekking Derived blow-ups
23.11 Marc Hoyois Bivariant theories
30.11 Marc Hoyois The section, formal group law, and strict normal crossings axioms
07.12 Massimo Pippi Precobordism and precobordism with line bundles
14.12 Denis Nardin The formal group law of precobordism
21.12 Niklas Kipp The universal property of precobordism and cobordism
11.01 Pavel Sechin Chern classes and the splitting principle
18.01 Charanya Ravi The Conner–Floyd and Riemann–Roch theorems
01.02 Toni Annala The algebraic Spivak theorem