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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
3
votes
Exotic automorphisms of the fundamental group of a curve?
Just a non-thought-out thought:
For any finite simple group $S$, consider the set of maps from $\pi$ to $S$ up to conjugacy. Now, $\mathrm{Out}(\widehat{\pi})$ acts on this set. Now consider the com …
21
votes
Algebraic Geometry versus Complex Geometry
Here is one I am curious about : Suppose X is a proper variety over $\mathbb{C}$. Then there are only finitely etale covers of X in each degree.
This is proven in SGA 1 by comparison with the clas …