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location | ||
age | ||
visits | member for | 3 years, 11 months |
seen | Jan 3 at 9:16 | |
stats | profile views | 3,180 |
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. |