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visits member for 3 years, 11 months
seen Jan 3 at 9:16
I'm interested in many things, but algebraic geometry I love.

Nov
23
asked General cohomology groups and motives
Nov
18
awarded  Popular Question
Nov
16
accepted Did Grothendieck have a plan for proving Riemann Existence algebraically?
Nov
15
awarded  Nice Question
Nov
14
awarded  Popular Question
Nov
13
comment Did Grothendieck have a plan for proving Riemann Existence algebraically?
No, Grothendieck's vision definitely did not come to fruition. When Grothendieck thought about this he envisioned the proof as going through the category of motives, and specifically through the standard conjectures (some of which remain open to this day).
Nov
13
awarded  Good Question
Nov
13
awarded  Nice Question
Nov
13
revised Did Grothendieck have a plan for proving Riemann Existence algebraically?
added 15 characters in body
Nov
13
comment Reference Request: Riemann's Existence Theorem
@Ariyan: I doubt that it is constructive even for affine regular schemes. Otherwise one would have an algebraic proof that $\pi_1(\mathbb{P}^1\smallsetminus a_1,...,a_r)\cong$ the profinite completion of $\langle \alpha_1,...,\alpha_r|\alpha_1 ...\alpha_r =1\rangle$.
Nov
13
asked Did Grothendieck have a plan for proving Riemann Existence algebraically?
Oct
31
comment Does a curve have infinitely many $K$-rational points under these hypotheses?
You're right. But that's just as easy.
Oct
31
accepted Does a curve have infinitely many $K$-rational points under these hypotheses?
Oct
31
comment Does a curve have infinitely many $K$-rational points under these hypotheses?
Well, that was way easier than I expected...
Oct
31
comment Does a curve have infinitely many $K$-rational points under these hypotheses?
I've made the body of the question reflect this.
Oct
31
revised Does a curve have infinitely many $K$-rational points under these hypotheses?
added 71 characters in body
Oct
31
comment Does a curve have infinitely many $K$-rational points under these hypotheses?
Yes, that's what I meant.
Oct
31
asked Does a curve have infinitely many $K$-rational points under these hypotheses?
Oct
25
asked In what way do the Weil Conjectures pertain to Langlands?
Oct
23
comment What are non-abelian $L$-functions?
I know very little about this, so my ability to elaborate is limited. I agree that L-functions can deal with non-abelian extensions. But it is also true that their definition goes through cohomology. I imagine that the "non-abelian" part of "non-abelian L-functions" has to do with their construction, and not with their applications. As for in what sense they would be stronger than the usual L-functions, this is part of my question.