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#### Seminar des SFB/TRR 326 GAUS

„Analytische Kohomologie von Lubin – Tate (φ, Γ)-Moduln“
Dr. Rustam Steingart, Universität Heidelberg

Let $L$ be a finite extension of $\mathbb{Q}_p.$ Lubin-Tate $(\varphi_L,\Gamma-L)$-modules are a tool used to study $L$-linear Galois representations but unlike in the classical case, where every Galois representation is overconvergent and hence can be described by a $(\varphi,\Gamma)$-module over the Robba ring whose $\Gamma$-action is $\mathbb{Q}_p$-analytic, the picture looks different in the Lubin-Tate case. Not every $(\varphi_L,\Gamma_L)$-module is overconvergent and the $\Gamma_L$-action is not automatically $L$-analytic. I will be presenting the main results of my thesis concerning the perfectness of $L$-analytic cohomology of Lubin-Tate $(\varphi_L,\Gamma_L)$-modules over relative Robba rings and an analogue of Shapiro's Lemma in this situation. I will also explain some applications of these results.

Freitag, den 11. November 2022 um 13.30 Uhr, in INF 205, SR A Freitag, den 11. November 2022 at 13.30, in INF 205, SR A

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