Classification theorems for vector bundles on the Fargues-Fontaine curve

Abstract: The Fargues-Fontaine curve has played a pivotal role in the recent development of arithmetic geometry. Most notably, the work of Fargues-Scholze constructs the local Langlands correspondence in a form of the geometric Langlands correspondence for the Fargues-Fontaine curve. In addition, Fargues shows that the Fargues-Fontaine curve provides a geometric interpretation for Galois cohomology of local fields and much of the classical p-adic Hodge theory.

In this talk, we discuss several classification theorems for vector bundles on the Fargues-Fontaine curve. In particular, we give a complete classification of all subsheaves, quotients, and minuscule modifications of a given vector bundle on the Fargues-Fontaine curve. We also discuss some applications of these theorems in the context of the local Langlands correspondence.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar