bio | website | |
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location | ||
age | ||
visits | member for | 4 years, 4 months |
seen | Jan 3 at 9:16 | |
stats | profile views | 3,277 |
I'm interested in many things, but algebraic geometry I love.
Dec 11 |
accepted | Where was Riemann Existence first proven? |
Dec 10 |
comment |
Where was Riemann Existence first proven?
I meant the following: any topological cover of an algebraic variety defined over the complex numbers can be given an algebraic variety structure such that the covering map is algebraic. |
Dec 10 |
asked | Where was Riemann Existence first proven? |
Nov 24 |
comment |
General cohomology groups and motives
@Daniel: While I agree that this seems to have no clear answer and is therefore worthy of closing down, I completely disagree that MO should not be the first place to go to with this sort of question. It is precisely the collective knowledge of mathematicians that I want to tap into. There is clearly no book about this; if there are papers about it they would be hard to find; and if individuals don't know the answer it doesn't mean that an answer doesn't exist. This is precisely what mathoverflow is for. |
Nov 24 |
comment |
General cohomology groups and motives
@Daniel: Alas, I did not. My understanding of Langlands is rudimentary at best. I was trying to place Langlands, which is a statement about Galois actions on certain groups coming from schemes, in the context of general Galois actions on groups coming from schemes. |
Nov 24 |
comment |
General cohomology groups and motives
@Daniel: that's a very good point. Does $H^i(X,\mathbb{Q}_p)$ being automorphic imply anything of any content about the representation $H^i(X,\mathbb{Z}/p^n\mathbb{Z})$? |
Nov 23 |
comment |
General cohomology groups and motives
I'm not sure if lisse l-adic sheaf is really what I would be looking for. Ideally, I would like a statement that would also make sense for $\mathcal{F}$ a linear algebraic group scheme (which would restrict us to non-abelian cohomology), although that might be asking too much. For now it would suffice to restrict ourselves to sheaves into abelian groups. |
Nov 23 |
comment |
General cohomology groups and motives
Hmm... I was careless with my speech. You are right that I meant $\mathcal{F}$ as sheaf on the etale site on $X$ rather than $X$. (I viewed that as implicit by the fact that I look at $H_{et}^*(X,\mathcal{F})$.) Your other comment is more substantive -- is it true that $H^i_{et}(X,\mathbb{Q}_p)$ where $\mathbb{Q}_p$ is the constant sheaf on the etale site over $X$ is different from the inverse limit of the $H^i_{et}(X,\mathbb{Z}/p^i\mathbb{Z})$? |
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. |