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

„Lifts of Cycle Classes of Sections of p-adic Curves“
Dr. Johannes Schmidt, Universität Heidelberg

Let $X/k$ be a smooth projective curve of genus $>1$ over a $p$-adic field $k$ together with a continuous section of the canonical map from the étale fundamental group of $X$ to the absolute Galois group of $k$. Esnault and Wittenberg associated to each such section a cycle class in the étale cohomology of $X$ and showed that it is algebraic in $\ell$-adic cohomology for $\ell\neq p$. The $p$-adic section conjecture predicts that this cycle class admits a canonical lift to the $\ell$-adic cohomology of any reduction of the curve $X$. Studying the étale homotopy type of a sufficiently nice reduction, we give a construction for such a canonical lift of the cycle class, giving a partial answer to a question of Esnault and Wittenberg.

Freitag, den 24. Juni 2016 um 13:30 Uhr, in INF205, SR C Freitag, den 24. Juni 2016 at 13:30, in INF205, SR C

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