Remi Reboulet (Université Grenoble Alpes)
tba

In this talk, I am going to explain the main results of my recent preprint (arXiv:2105.12591). The primary goal will be to prove that for every affinoid analytic adic space $X$, pseudocoherent complexes, perfect complexes, and finite projective modules over $\mathcal{O}_X(X)$ form a stack with respect to the analytic topology on $X$. The proof relies on the new approach to analytic geometry developed by Clausen and Scholze by means of condensed mathematics; therefore, I will also explain how to apply their formalism of condensed analytic rings to the study of adic geometry.

We give an outline of a (conjectural) construction of cohomology groups for smooth and proper varieties over local fields with values in the derived category of locally compact groups satisfying a Pontryagin duality. For certain weights, we give an ad hoc construction which satisfies such a duality unconditionally. We then explain how this leads to … Continue reading Thomas Geisser (Rikkyo University Tokyo): Duality for motivic cohomology over local fields and applications to class field theory →