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bio website people.brandeis.edu/~jbellaic
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visits member for 3 years, 11 months
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Professor of Mathematics at Brandeis University


Aug
18
comment Kernel of the character of congruence groups
Dear Abdullah, I have slightly edited your question in order to introduce the precisions you gave in comments.
Aug
18
revised Kernel of the character of congruence groups
I introduced in the text of the question the precisions given in comments by the OP
Aug
17
answered Why considering schemes over discrete valuation rings?
Aug
14
comment Smallest prime in an arithmetic progression
And it is conjectured that much more that even what can be proved using GRH is true, namely that the first prime is O(b^{1+\epsilon}) for all $\epsilon>0$, or perhaps even $O(b \log^2b)$.
Aug
14
reviewed Leave Open Chow group of zero-cycles generated by open dense subscheme
Aug
14
reviewed Leave Open The ten martini problem - reason for name
Aug
14
comment The Modularity Theorem and Serre's/Faltings's Isogeny Theorem
Vesselin, you could post your comment as an answer.
Aug
14
awarded  Necromancer
Aug
14
awarded  Nice Question
Aug
13
revised Effective Chebotarev without Artin's conjecture
edited body
Aug
7
revised The cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$
added 28 characters in body
Aug
7
comment The cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$
You're right. I correct.
Aug
7
revised The cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$
added 5 characters in body
Aug
7
answered The cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$
Aug
6
comment Faithful representations of free pro-p groups
Ah yes, you're right. Sorry.
Aug
6
comment Faithful representations of free pro-p groups
Pablo, what is stated without proof? I don't see your exact result stated, but Theorem 1.1 is the same with $\overline{ \mathbb Q_p}$ replaced by a local field, and it is proved in the paper. To go from the case of a local field to your case, you just have to know, as you said yourselves in your question, that since $F(p,m)$ is compact its image is in $GL_n(F)$ for a local field $F$. Of course, the proof of Theorem 1.1 in the paper is not long (two paragraphs) but it is a proof all the same (using a result of Pink, whose proof you can find in the reference given).
Aug
5
comment Computer Science applications of Roth's Theorem
It's a very strange question. You know well enough that most subjects in pure mathematics are not developed in view of applications and many do not have at this time (and perhaps will never have) any application. Now it might be possible that the subject of additive combinatorics has some application to CS, and I would understand you asking about tis, but restricting the question to one single theorem in Additive Combinatorics, for no other reason that you have studied this theorem, makes it pointless. Like "what are the applications of Zhang's theorem on bound between primes to biology?"
Aug
2
awarded  Good Question
Aug
1
comment mod $p$ Jacquet-Langlands correspondence
Dear user56638, I don't know a reference for any of these cases. The study of mod $p$ representations of reductive groups over a local field $F$ in the case where $p$ is not the residue characteristic of $F$ has been the object of a lot of attention in the 80's, 90's and early 2000's, but I don't know where the case of the group of units of a central simple algebra is treated. You should look carefully in the work of M.-F. Vignéras.
Jul
31
comment mod $p$ Jacquet-Langlands correspondence
Is the residue characteristic of $F$ equals to $p$, or different from $p$? That's two cases which are very different...