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Apr
6
comment Any heuristics explaining why one seems to have $2n=p+q\Rightarrow\pi(p)+\pi(q)=Li(2n)+o(1)$?
I mean, it is an iterating test of the power of our theory whether it can easily disprove wacky conjectures...
Apr
6
comment Any heuristics explaining why one seems to have $2n=p+q\Rightarrow\pi(p)+\pi(q)=Li(2n)+o(1)$?
Or perhaps we can't disprove it due to our bad knowledge on the Goldbach problem. But then what about this one. Conjecture: there exist $C,D>0$ such that for all odd integers $n$, and all triples of primes $(p,q,r)$ such that $p+q+r=n$ excepts at most $C$ of them, $| \pi(p) + \pi(q) + \pi(r) - Li(n)| \leq D$. Again, I would say it is surely false, but could one disprove it?
Apr
6
comment Any heuristics explaining why one seems to have $2n=p+q\Rightarrow\pi(p)+\pi(q)=Li(2n)+o(1)$?
I find the question interesting, at least if it would be made as a precise conjecture, for example what about this weakening of the conjecture: there exists $C,D>0$ such that for all integers $n$, and all pairs of primes $(p,q)$ such that $p+q=2n$ excepts at most $C$ of them, $| \pi(p) + \pi(q) - Li(2n)| \leq D$. I would say it is surely false, but could one disprove it?
Feb
26
comment Galois representations along eigenvarieties
1. Yes, for what you say, plus the fact that after a blow-up you can make your torsion-free sheaf locally free. 2. My paper at Duke "non-smooth classical point on eigenvarieties", contains an example of a point on eigenvariety where the pseudo-character is proven not to come from a representation over a locally-free sheaf, even Zariski-locally around this point, and even after restriction to an irreducible component. The heuristics seems to be that when the geometry of the eigenvariety is too nasty (typically, not locally UFD), the pseudo-characters tends not to come with a loc.-free sheaf.
Feb
22
comment Galois representations along eigenvarieties
Dear David, it seems to me that you're answering a slightly different question than the one the OP asked -- but perhaps you're answering what he really meant. The OP writes he wants a locally-free sheaf on a cover (with a Galois action) and doesn't say he want them canonical. It seems that your answer aims at giving a canonical coherent sheaf with a Galois action, which is a different (and quite interesting) question.
Feb
22
answered Galois representations along eigenvarieties
Feb
20
comment When a journal doesn't give your work a fair chance
I have seen this happening in at least one case (where I was not directly involved) in pure mathematics, at one of the very top journal.
Feb
19
comment A presentation for $GL(2,\mathbb{Z}/p^n \mathbb{Z})$
There is something wrong with your presentation. Since $a,b$ have determinant $2$ and $1$, all their powers have determinant a power of $2$. If $2$ is a square modulo $p$, this implies that $a,b$ is not a system of generator.
Jan
18
comment Analogue of Tate curve for $g>1$
+1 for the pseudo.
Jan
2
awarded  Nice Answer
Dec
31
reviewed Leave Open Will any two linearly equivalent ample divisors on an abelian variety intersect?
Dec
19
comment Grothendieck's “List of classes of structures”
I like your question, and I love your picture.
Dec
15
awarded  Necromancer
Dec
15
revised Definition of CM modular form
Corrected spelling.
Dec
5
awarded  Popular Question
Nov
28
comment All compact surfaces $S\subseteq \mathbb{R}^3$ are rigid?
Interesting question, +1. In view of the comments and answers, it seems safe to add the tag "open problem" to the question, but being no differential geometer, I would not do that myself.
Nov
12
awarded  Good Answer
Nov
7
awarded  Nice Answer
Nov
7
answered What are some very important papers published in non-top journals?
Nov
2
comment For a linear recurrence sequence $(u_n)_{n\geq 0}$, can $\{i \mid u_i > 0\}$ be the set of Fibonacci numbers?
Michaël, thanks a lot. I was asking for the second part. I'll check out the book by Salomaa and Soittolam it looks very interesting. I have recently been using the generalization in characteristic p by Derksen of the Skolem-Mahler-Leech theorem, and grew very interested in this set of questions...