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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)

Zoom

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 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

Plectic Stark-Heegner points (after Fornea-Gehrmann and Fornea-Guitart-Masdeu)

Heidelberg, Mathematikon, SR A and Livestream

We will meet on Tuesdays at 9:15 in SR 8 in the Mathematikon, Heidelberg. The seminar is planned to be in person, but it will also be possible to participate online (more details will follow later). Attached to this email you can find the program. If you are interested in giving a talk, please send … Continue reading Plectic Stark-Heegner points (after Fornea-Gehrmann and Fornea-Guitart-Masdeu)

Free

Georg Tamme (Universität Mainz): Purity in chromatically localized algebraic K-theory

Heidelberg, Mathematikon, SR A and Livestream

In classical algebra, the prime fields are Q and for every prime number p the finite field F_p. In higher algebra, one has for every prime number p an additional sequence of prime fields K(p,n), n a natural number, which in some sense interpolates between Q and F_p. Associated with these prime fields one has … Continue reading Georg Tamme (Universität Mainz): Purity in chromatically localized algebraic K-theory

Hodge theory of matroids (Session 2)

Zoom

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 can deal with this problem by applying a rigid-geometric point of view: for a formal scheme X of finite type over a complete rank one valuation ring, … Continue reading Dr. Marcin Lara: Specialization for the pro-étale fundamental group and fundamental groups in rigid geometry