Morava motives and Galois cohomological invariants

Date(s)
Wednesday 13th November 2024 (14:00-15:00)
Contact
Event Convenor Contact: Hamid.Abban@nottingham.ac.uk
Description
Speaker's Name: Pavel Sechin
Speaker's Affiliation: University of Regensburg
Speaker's Research Theme(s): Pure Mathematics,
Abstract:
Galois cohomology is a sequence of abelian groups that is associated to a field K and are non-trivial only if the field K is not algebraically closed. Given an algebraic variety over a field K, one could consider its invariants that take values in Galois cohomology of K. Since these invariants would vanish over the algebraic closure of K, this would be especially meaningful if the variety also 'trivializes' over the algebraic closure, i.e. becomes of some 'simple' or 'canonical' form. There are, however, many other cases which are not captured by this scheme, and there is no known universal definition of Galois cohomological invariant. In my talk, I will present a framework in which one can work with Galois cohomology (of arbitrary fixed degree) and smooth projective varieties on the same footing. In this setting the definition of Galois cohomological invariant of an arbitrary smooth projective variety becomes almost a tautology. In order to define this framework one needs to mix the ideas of Grothendieck motives with the algebro-geometric part of the chromatic homotopy theory, namely, Morava K-theories. The talk is based on work in progress, partially joint with A.Lavrenov.

Venue: Physics C04

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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