Analytic K-theory Learning Seminar, 2024

This is a learning seminar on the recent notion of analytic K-theory of analytic adic spaces. The goal is to understand the definition of analytic K-theory using the notion of nuclear modules, and then prove a version of the Grothendieck-Riemann-Roch Theorem for rigid-analytic varieties. The main reference is the PhD thesis of Greg Andreychev available here.

The seminar meets on Fridays 2:30pm--4:30pm at Fine Hall 314 (Princeton).

Organizers: Greg Andreychev, Vadim Vologodsky, and Bogdan Zavyalov

Syllabus

Schedule

Spring
1 January 26 G. Andreychev Introductory Talk .pdf
2 February 2 M. Morrow Recollections on K-theory .pdf
3 February 9 A. Krause Dualizable Categories .pdf
4 February 16 J. Lurie Efimov K-theory .pdf
5 February 23 G. Bosco Analytic Animated Rings .pdf
6 March 1 T. Moulinos Trace Class Maps and Nuclearity .pdf
7 March 22 S. Howe Analytic Adic Spaces and Descent .pdf
8 April 2 J. E. Rodriguez Camargo Solid 6-functor Formalism in Non-Archimedean Analytic Geometry .pdf
9 April 5 E. Reinecke Nuc(X) is dualizable .pdf
10 April 12 L. Tang Nisnevich Descent for K-theory .pdf
11 April 19 S. Gilles Etale Hyperdescent .pdf
12 April 26 V. Vologodsky Grothendieck-Riemann-Roch, Part I
13 May 3 M. Kubrak Grothendieck-Riemann-Roch, Part II .pdf

Useful links:

1) Condensed math:

[CS] Lectures on Condensed Mathematics (aka the first condensed lecture notes), D. Clausen and P. Scholze
[CS2] Lectures on Analytic Geometry (aka the second condensed lecture notes), D. Clausen and P. Scholze
[A1] Pseudocoherent and Perfect Complexes and Vector Bundles on Analytic Adic Spaces, G. Andreychev

2) K-theory:

[Heb] Lecture Notes for Algebraic and Hermitian K-Theory, F. Hebestreit
[Hoy] K-Theory of Dualizable Categories (After A. Efimov), M. Hoyois
[Cla] IHES Lectures on Efimov K-theory, Lecture 1, Lecture 2, Lecture 3, D. Clausen

3) K-theory of adic spaces and Grothendieck-Riemann-Roch:

[A2] K-Theorie adischer Raume, G. Andreychev
[CS3] Condensed Mathematics and Complex Geometry (aka the third condensed lecture notes) [the relevant material is Lectures XIV and XV], D. Clausen and P. Scholze