EVENT DETAILS AND ABSTRACT

Title: Algebraic and geometric cobordism
Speaker: Toni Annala
Speaker Info: IAS
Brief Description:
Special Note:
Abstract:

In my thesis, I constructed a cohomology theory of schemes called algebraic cobordism Ω^*, extending the similarly named theory of Levine--Morel from smooth varieties in characteristic 0 to all finite-Krull-dimensional Notherian schemes admitting an ample line bundle. This is a non-A^1-invariant cohomology theory that is closely related to the (higher) algebraic cobordism MGL that is constructed in recent work with Marc Hoyois and Ryomei Iwasa. In particular, we expect that Ω^n(X) = MGL^{2n,n}(X) whenever both sides are well defined. I will discuss results about Ω^* related to this comparison, and explain why obtaining the desired isomorphism, or an interesting weakening of it, seems hopeless unless someone has a smart idea, or alternatively someone proves resolution of singularities in positive characteristic.