bio | website | math.u-psud.fr/~chambert |
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location | Université Paris-Sud (Orsay) | |
age | 44 | |
visits | member for | 5 years, 4 months |
seen | Aug 24 at 10:34 | |
stats | profile views | 3,662 |
Jul
6 |
comment |
About Abhyankar's conjecture
The statement you give is Raynaud's contribution. Harbater's theorem is for covering of arbitrary algebraic curves — it says that a group $G$ is the Galois group of a covering of a curve (genus $g$, minus $r$ points) over an algebraically closed field of characteristic $p$ iff its quotient $G/p(G)$ by the subgroup $p(G)$ generated by $p$-subgroups is such a group. By Grothendieck the latter property means that it is a quotient of the fundamental group of a compact Riemann surface of genus $g$ deprived of $r$ points. |
Jul
5 |
comment |
Volume of arithmetic quotients of symmetric spaces
The deck transformation group preserves the measure. See Paul Garrett's answer. |
Jul
5 |
comment |
Volume of arithmetic quotients of symmetric spaces
I am a bit puzzled by the amount of notation, but look at the canonical map from $\Gamma(\mathfrak P^{ek})\backslash G_\infty$ to $\Gamma\backslash G_\infty$. It should be a (possibly ramified) covering of degree $[G:G_k]$, and this should imply your claim. |
Jul
2 |
comment |
N-th root of unity in N-th division field of abelian variety?
@JoeSilverman: Unfortunately, I made a confusion and (see Zarhin's comment above), it is $(A\times A^{\vee })^4$ which is principally polarized. |
Jul
2 |
comment |
N-th root of unity in N-th division field of abelian variety?
My mistake! Sorry for the confusion and thank you for your answer and your reply to my comment. |
Jul
1 |
comment |
N-th root of unity in N-th division field of abelian variety?
It seems that one can also combine Joe Silverman's answer with your observation that $A^4$ has a principal polarization. |
Jul
1 |
comment |
N-th root of unity in N-th division field of abelian variety?
But one knows (“Zarhin's trick”) that $A^4$ has a principal polarization. Since $K(A[n])=K(A^4[n])$, this implies that the result holds in general! |
Jun
12 |
comment |
When does a modular form satisfy a differential equation with rational coefficients?
@DrorSpeiser: You're right, sorry. I misunderstood your question. |
Jun
6 |
comment |
discrete valuation ring and ring of witt vectors
Notation: In the context of Witt vectors, the field with $p$ elements should definitely not be denoted by $\mathbb Z_p$! |
Jun
2 |
awarded | Nice Answer |
Jun
1 |
answered | Solving algebraic problems with topology |
May
14 |
comment |
Group schemes, adeles, double cosets, and étale cohomology
In my paper with Yuri Tschinkel, Torseurs arithmétiques et espaces fibrés, we have a similar description (Proposition 1.2.6). NB. As remarked by Philippe Gille, there is a slight mistake there, that we consider torsors which are locally trivial for the Zariski topology, without saying so. |
May
11 |
comment |
Irreducible/prime/indivisible elements
The product of <= 1 field does not admit prime elements. |
Apr
24 |
comment |
Constants sheaves on an open subset
Actually, the formulation of the question is incorrect, which led to the two different answers. You write that $\mathbb Z_U$ is a sheaf on $U$, while $F$ is a sheaf on $X$; so $\mathop{\rm hom}(\mathbb Z_U,F)$ does not make sense. You must either restrict $F$ to $U$ or extend $\mathbb Z_U$ to $X$. In the first case, the answer is yes (Zhen Lin's comment), and in the second it depends on the choice of an extension (direct image or extension by zero). |
Apr
22 |
comment |
Base change of regular schemes
And if you want an equal-characteristic example, take $R=\mathbf C[[t]]$ and $X$ be the closed subscheme of $\mathbf A^2_R$ defined by $xy=t$; it is regular, but its base change to $\mathbf C[[t^{1/2}]]$ is not. |
Apr
20 |
comment |
Must an algebraic variety with trivial tangent bundle be an abelian variety?
And no if you don't assume some properness condition. |
Apr
18 |
revised |
Reference for a lemma on étale maps
Typo. tale->étale |
Apr
17 |
comment |
Reference for a lemma on étale maps
With all due respect to the established litterature, the Stacks project cannot be considered less respectable than anything else published. |
Apr
15 |
comment |
Interpretation of the monomorphism $H^2(\pi_1(X),\mathbb{Z}) \rightarrow H^2(X,\mathbb{Z})$
What about removing the zero-section and considering its fundamental group? |
Apr
15 |
awarded | Yearling |