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Seminar
FIELD Math: CMC
DATE October 22 (Thu), 2020
TIME 10:00-11:30
PLACE Online
SPEAKER Hong, Serin
HOST Kim, Chan-Ho
INSTITUTE University of Michigan
TITLE [Number Theory] Quotients, subsheaves and extensions of vector bundles on the Fargues-Fontaine curve
ABSTRACT Since its construction in early 2010s, the Fargues-Fontaine curve has played a pivotal role in p-adic Hodte theory and related fields. Vector bundles on this ``curve" are of particular interest, as they provide a geometric interpretation of numerous constructions from those fields. Most notably, by the upcoming work of Fargues-Scholze, the local Langlands correspondence can be realized in terms of certain sheaves on the stack of vector bundles on the Fargues-Fontaine curve. In this talk, we discuss several classification theorems about vector bundles on the curve, including a complete classification of quotients and subsheaves of a given vector bundle. Our proof crucially relies on Scholze's theory of diamonds, which provides a correct framework for dimension counting of various moduli spaces of bundle maps.
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