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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 …
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 …