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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

7 votes

The congruence subgroup property for mapping class groups and a conjecture of Grothendieck

Let $K$ be a field of characteristic zero, $X/K$ a hyperbolic $(g,n)$-curve. There is a famous short exact sequence $$1\longrightarrow\pi_1(X\otimes \overline{K})\longrightarrow\pi_1(X)\longrightarrow …
coLaideronnette's user avatar
13 votes
3 answers
1k views

$\ell$- vs. $p$-adic and de Rham vs. Betti in the geometric Langlands correspondence

In Emerton–Gee–Hellmann’s IHÉS notes on the categorical $p$-adic local Langlands programme, one finds the following remark: The differences between the $\ell$-adic and $p$-adic settings are reminisce …
coLaideronnette's user avatar