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50 votes
1 answer
15k views

Consequences of Geometric Langlands

So, lots of people work on the Geometric Langlands Conjecture, and there have been a few questions around here on it (admittedly, several of them mine). So here's another one, tagged community wiki ...
12 votes
1 answer
1k views

Relation between motives and geometric Langlands

When working over a number field (or a function field over a finite field), one predicts that the Langlands program is related to the theory of motives over this field. There are several ways I have ...
JustLikeNumberTheory's user avatar
3 votes
0 answers
202 views

What d.o. $\sum_i f_i(z)\partial_z^i$ correspond to subalgebras $M$ in polynoms $C[x_i]$ being Langlands dual to motive of $Spec(M) \to X$?

Briefly: The question is about presenting explicit examples of the construction discussed in the recent MO question "Relation between motives and geometric Langlands" and Will Sawin's asnwer ...
Alexander Chervov's user avatar
20 votes
1 answer
2k views

LMS Lectures on Geometric Langlands

Everybody knows how insightful are David Ben-Zvi talks (and comments/answers here on mathoverflow). I was trying to watch the LMS 2007 Lecture Series on Geometric Langlands by David, supposedly made ...
Carlos's user avatar
  • 653
11 votes
2 answers
1k views

Examples of Eigensheaves outside of langlands

In geometric Langlands, one looks at correspondences of the form $$ Bun_n(X) \leftarrow Hecke \rightarrow X\times Bun_n(X)$$ and calls a sheaf on the lefthand space Hecke eigensheaf, if pulling ...
Jan Weidner's user avatar
  • 13.2k