Landweber-equivariant Grothendieck motives: a toy example of non-oriented phenomena

by Pavel Sechin (Universität Regensburg)

Thursday 12 Nov 2020, 12:30 → 14:30 Europe/Moscow

958-115-833 (Zoom)

Landweber-equivariant motives are constructed as a limit of a diagram of categories of Grothendieck motives associated to oriented cohomology theories (such as algebraic cobordism, Chow groups and K-theory) with functors of Riemann-Roch type between them. Thus constructed category is computable to the same degree as algebraic cobordism, but it possesses some non-oriented properties, e.g. a motive of a projective space does not decompose anymore as a direct sum of 'Tate motives' and the dual of a motive of a smooth projective variety involves a non-trivial twist along the class of the tangent bundle in K-theory. This category has an exact structure, and many (or maybe all, to an extent) direct sum decompositions in Chow motives (e.g. projective bundle decomposition or a blow-up along a smooth subvariety decomposition) lift to non-trivial extensions in this category.

I will explain the construction and the properties of Landweber-equivariant motives, but at the moment there are no applications.

Notes from the talk Video