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

9 votes
1 answer
1k views

What analysis should I know for studying Arakelov Theory?

Hi! I have a fairly good background in Algebraic Geometry (say at the level of Hartshorne's book and some Intersection Theory from Fulton) and since I think working over $\text{Spec } \mathbb{Z}$ is …
24 votes
3 answers
2k views

Explicit computations of the étale homotopy type?

Hi, I'm currently trying to learn about etale homotopy for schemes as introduced by Artin-Mazur. I know that by the Artin-Mazur comparision theorem, it is possible to compute the etale homotopy type …
5 votes
2 answers
514 views

Essential geometric morphisms on the étale site.

Hi! There is a risk that this question might be utterly trivial, and if it is, my sincerest apologies, but I haven't been able to find anything in the literature. Let $f:X \rightarrow Y$ be an étal …
42 votes
7 answers
30k views

Undergraduate roadmap to algebraic geometry?

Hello, I'm sorry if this question isn't posted correctly. I hope that it is (since other questions regarding roadmaps have been allowed). Now to my question: From what I've heard from professors and …