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Results tagged with ag.algebraic-geometry
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user 4351
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
7
votes
Accepted
Abelian varieties as analytic manifolds
Yes, this is true. For any smooth finite type $k$-scheme $X$, $k$ a non-Archimedean field, $X(k)$ has a canonical structure of $k$-analytic manifold in the sense of Serre's book (or Bourbaki). Usually …
- 3,380
6
votes
Scheme-theoretic account of why every variety embeds in a complete variety
Brian Conrad has a writeup on this:
http://math.stanford.edu/~conrad/papers/nagatafinal.pdf
- 3,380
7
votes
Accepted
Relation between partially computable function and complex function
Any complex-valued function on $\mathbb{N}$ can be extended to an entire function, so the answer is "yes." This follows from Theorem 15.13 of Rudin's Real and Complex Analysis, which states that for a …
- 3,380
23
votes
Roadmap for studying arithmetic geometry
If you can find a (say, library) copy of Cornell and Silverman's Arithmetic Geometry I would highly recommend it. It is a comprehensive treatment of the arithmetic theory of abelian varieties using th …