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Grigory Andreychev (Universität Bonn): Descent on Analytic Adic Spaces via Condensed Mathematics

Heidelberg, Mathematikon, SR A and Livestream

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.

Hodge theory of matroids (Session 1)

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This semester’s topic in our joint research seminar is Hodge theory of matroids. The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.
Talk 1: Overview of the topic of the seminar. (Martin Ulirsch)
Talk 2: Matroid basics I – cryptomorphisms and examples (Ingmar Metzler)

Thomas Geisser (Rikkyo University Tokyo): Duality for motivic cohomology over local fields and applications to class field theory

Heidelberg, Mathematikon, SR A and Livestream

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 … Continue reading Thomas Geisser (Rikkyo University Tokyo): Duality for motivic cohomology over local fields and applications to class field theory

Hodge theory of matroids (Session 2)

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The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.
Talk 3: Matroid basics II – exercise session (no speaker)
Talk 4: Matroid basics III – the lattice of flats (Arne Kuhrs)

Dr. Marcin Lara: Specialization for the pro-étale fundamental group and fundamental groups in rigid geometry

Heidelberg, Mathematikon, SR A and Livestream

The specialization morphism for the étale fundamental groups of Grothendieck cannot be generalized word-for-word to the more general pro-\'etale fundamental group of Bhatt and Scholze. It turns out, that one … Continue reading Dr. Marcin Lara: Specialization for the pro-étale fundamental group and fundamental groups in rigid geometry