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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 …
Myshkin's user avatar
  • 17.6k
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 …
moonface's user avatar
  • 748