Joël
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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...