Speaker: Pavel Sechin
Date: March 26, 2026
Affiliation: University of Regensburg, Germany

Abstract: For a field $k$, one tries to understand its absolute Galois group via Galois cohomology with finite coefficients $H(k, Z/p^r)$, where $p$ is a prime number. Although this invariant is defined purely algebraically, one of the most efficient tools for its study are algebraic cycles on some `arithmetically interesting' algebraic varieties over $k$. For example, by the work of Rost, it was known how to control the vanishing of certain special elements in $H(k, Z/p)$, `symbols', via the group of $0$-cycles on associated Rost varieties. I will explain how the use of the algebraic Morava $K$-theory and motives permits to control arbitrary elements in $H(k, Z/p^r)$ for all $r$.