اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRemarks on cycle classes of sections of the arithmetic fundamental group
166
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Given a smooth and separated K(pi,1) variety X over a field k, we associate a cycle class in etale cohomology with compact supports to any continuous section of the natural map from the arithmetic fundamental group of X to the absolute Galois group of k. We discuss the algebraicity of this class in the case of curves over p-adic fields, and deduce in particular a new proof of Stixs theorem according to which the index of a curve X over a p-adic field k must be a power of p as soon as the natural map from the arithmetic fundamental group of X to the absolute Galois group of k admits a section. Finally, an etale adaptation of Beilinsons geometrization of the pronilpotent completion of the topological fundamental group allows us to lift this cycle class in suitable cohomology groups.
قيم البحث
اقرأ أيضاً
Let $mathcal{X}$ be a regular projective arithmetic variety equipped with an ample hermitian line bundle $overline{mathcal{L}}$. We prove that the proportion of global sections $sigma$ with $leftlVert sigma rightrVert_{infty}<1$ of $overline{mathcal{
L}}^{otimes d}$ whose divisor does not have a singular point on the fiber $mathcal{X}_p$ over any prime $p<e^{varepsilon d}$ tends to $zeta_{mathcal{X}}(1+dim mathcal{X})^{-1}$ as $drightarrow infty$.
We consider stacks of filtered phi-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an open substack
containing all classical points. Further we study a period morphism (defined by Pappas and Rapoport) from a stack parametrizing integral data and determine the image of this morphism.
We determine the cycle classes of effective divisors in the compactified Hurwitz spaces of curves of genus g with a linear system of degree d that extend the Maroni divisors on the open Hurwitz space. Our approach uses Chern classes associated to a g
lobal-to-local evaluation map of a vector bundle over a generic $P^1$-bundle over the Hurwitz space.
Let p be an odd prime number. We show that there exists a finite group of order p^{p+3} whose the mod p cycle map from the mod p Chow ring of its classifying space to its ordinary mod p cohomology is not injective.
We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. If a certain self-product of $X$ carries an
exotic Tate class then the self-product $X^{2N}$of $X$ also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
