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I'm interested in many things, but algebraic geometry I love.

Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
Look at the discussion above -- what you suggest will only make the condition hold at $x=a$, but not for other values of $x$. For example try multiplying $0,x,1,x+1$ (which satisfy the condition over $x=0$) by $(x-3)^2$ and see that there are values where some of these intersect with multiplicity $1$.
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
@Will: I want that all of its nonzero roots will have multiplicity $\geq m$. Furthermore, I want that for every $i$ there will exist a unique $j$ such that $0$ is a root of $f_i-f_j$.
Feb
12
revised Are there n polynomials for which all intersection multiplicities are at least m?
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Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
You're right! So I guess this proves the $m=2$, $n=4$ case. I can't see how this would generalize, though...
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
Let's do a quick example: $0,x,1,1+x$ have the desired property at 0. If $m=2$, you're saying to multiply by $(x-1)^2$, say. $1(x-1)^2$ and $x(x-1)^2$ indeed intersect with multiplicity $2$ at $x=1$, but they would also intersect with multiplicity $1$ at some $x\neq 0,1$. So that's undesirable.
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
@Mahdi: I don't see why that would solve it. It would just change the intersection number over $x=a$, but not over other values of $x$.
Feb
12
revised Are there n polynomials for which all intersection multiplicities are at least m?
added 141 characters in body; added 6 characters in body; added 44 characters in body
Feb
12
comment Are there n polynomials for which all intersection multiplicities are at least m?
Hmmm, let me clarify in the body of the question.
Feb
12
asked Are there n polynomials for which all intersection multiplicities are at least m?
Feb
4
answered Why should the anabelian geometry conjectures be true?
Jan
25
asked What is the obstruction for a local set of models of a curve to come from a global model?
Dec
25
awarded  Popular Question
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 $H^i_{et}(X,\mathbb{Z}/p^i\mathbb{Z})$?