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#### Seminar der Forschergruppe 'Symmetrie, Geometrie und Arithmetik'

„Chern classes from algebraic Morava K-theories“
Pavel Sechin, HSE Moskau

Algebraic Morava $K$-theories are generalized orientable cohomology theories which can be obtained from algebraic cobordism of Levine-Morel by the change of coefficients. The ring of coefficients of these theories is $\mathbb{Z}_{(p)}$ where $p$ is a prime number, and from a point of view of formal group laws Morava $K$-theories $K(n)$ lie 'in between' the $K$-theory of vector bundles $K_0$ and Chow groups. We will explain that there exist operations from $K(n)$ to many orientable theories (e.g. $K(mn)$ for natural $m$, and $CH^*\otimes\mathbb{Z}_{(p)})$ which are similar to Chern classes of vector bundles and called likewise. Chern classes from $K(n)$ to $K(n)$ allow to define the gamma filtration on Morava $K$-theories, and we will explain how one can use it to obtain estimates on torsion in Chow groups of some quadrics.

Freitag, den 5. Mai 2017 um 13:30 Uhr, in INF 205, SR A Freitag, den 5. Mai 2017 at 13:30, in INF 205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Alexander Schmidt