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Jun
8
comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth?
@YCor: Sorry for the inaccuracies. Did you mean $(b(r+1)-b(r))/b(r)=O(r^{-1})$?
Jun
8
comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth?
Is it possible to reduce the general case to the case of normal subgroups by taking a finite index normal subgroup of the not necessarily normal subgroup? I'm not sure - because running over different subgroups we get covers of unbounded degree (I mean: the Schreier graph of G/H covering the Cayley graph G/N for some N normal in G and contained in H).
Jun
8
comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth?
@YCor: Here's an idea: If the degree of the polynomial growth of $G$ is $d$, then (very nontrivially) the growth goes like $Cd^r$ for some constant $d$ (not only a upper bound, but almost exactly), and so the ratio $|\partial B(r)|/|B(r)|$ is at most $d/r$. For quotients the same is true with an even smaller (at least, not larger) degree $d$. Does this seem right? If so, then it settles the version of the question were we're only looking at quotients by normal subgroups, and we're left with generalizing to general subgroups (maybe this was obvious to you, I'm still a beginner in this field).
Jun
7
comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth?
@YCor: I know how to show that balls are Folner in groups of subexponential growth, but (the supremum version of) this question asks for more, doesn't it? I would like to know the answer too.
Jun
7
comment Is there a “uniform” Folner sequence consisting of balls for f.p. groups with polynomial growth?
@YCor: I too believe "supremum" was meant here, but note that $H$ only runs over finite index subgroups.
Mar
28
accepted Finite dimensional central division algebras over a finite extension of $\mathbb{F}_q(T)$
Mar
28
comment Finite dimensional central division algebras over a finite extension of $\mathbb{F}_q(T)$
@KCd: Do you have a reference for that?
Mar
28
asked Finite dimensional central division algebras over a finite extension of $\mathbb{F}_q(T)$
Mar
27
accepted Components in random graphs $G(n,p)$
Mar
24
asked Components in random graphs $G(n,p)$
Dec
27
awarded  Nice Question
Dec
20
awarded  Constituent
Dec
16
awarded  Caucus
Dec
16
accepted Bounds on eigenvalues of Hecke operator on the Jacobian
Dec
2
comment Bounds on eigenvalues of Hecke operator on the Jacobian
@BrunoJoyal: I guess that's $2g$ where $g$ is the genus of the curve. I need to think about it a little more.
Dec
2
comment Bounds on eigenvalues of Hecke operator on the Jacobian
You are right, I was confused (and now a little less). So, is the $l$-tate module ($l\neq p$) "suitable"? What is the dimension (lets tensor with $\mathbb{Q}_l$ to get a vector space).
Nov
28
revised Bounds on eigenvalues of Hecke operator on the Jacobian
added 21 characters in body
Nov
28
comment Bounds on eigenvalues of Hecke operator on the Jacobian
By the way, I'm thinking of the Jacobian as an abelian group: Divisors of degree zero modulo principal divisors. This is my starting point in this question.
Nov
28
revised Bounds on eigenvalues of Hecke operator on the Jacobian
deleted 1 character in body
Nov
28
asked Bounds on eigenvalues of Hecke operator on the Jacobian