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.

• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk