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.
Presenter: Serin Hong, University of Michigan
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