AbstractThe local Langlands correspondence is a conjectural relation between sets of smooth representations and Langlands parameters, which has recently been upgraded to categorical equivalences by Fargues-Scholze/Xinwen Zhu in two different ways. I will describe mywork in progress on comparing these two categories
AbstractMotivated from the categorical Torelli theorems, we introduce two types of infinitesimal categorical problems, connecting infinitesimal Torelli problems with a commutative diagram. Our constructions are general, and the main examples in this talk are nontrivial components of derived categories of Fano 3-folds. The infinitesimal categorical Torelli theorems for Fano 3-folds are summarize...
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