arXiv math/02122822002-12-19math.NTmath.RT

Representations non temperees pour U(3) et conjectures de Bloch-Kato

Joel Bellaiche, Gaetan Chenevier

备注：: 42 pages, LateX, french

英文摘要：

We use $p$-adic families of automorphic forms for an unitary group in three variables, containing some non-tempered forms constructed by Rogawski, to prove some cases of the Bloch-Kato conjectures.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux

We prove the local Gross-Prasad conjecture for tempered representations of special orthogonal groups. Roughly speaking, the conjecture says that, if sigma is an irreducible representation of SO(n) and rho is an irreducible representation of SO(n-1), rho appears as quotient of the restriction of sigma to SO(n-1) with a multiplicity m(sigma,rho) that can be computed in terms of epsilon-factors. Our proof uses results of a previous papers which computes m(sigma,rho) and the epsilon-factors by integral formulas.

2009-11-24math.NTmath.RT

La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes unitaires

Let $E/F$ be a quadratic extension of non-archimedean local fields of characteristic 0 and let $G=U(n)$, $H=U(m)$ be unitary groups of hermitian spaces $V$ and $W$. Assume that $V$ contains $W$ and that the orthogonal complement of $W$ is a quasisplit hermitian space (i.e. whose unitary group is quasisplit over $F$). Let $π$ and $σ$ be smooth irreducible representations of $G(F)$ and $H(F)$ respectively. Then Gan, Gross and Prasad have defined a multiplicity $m(π,σ)$ which for $m=n-1$ is just the dimension of $Hom_{H(F)}(π,σ)$. For $π$ and $σ$ tempered, we state and prove an integral formula f…

2012-12-04math.NTmath.RT

Autour d'une conjecture de Kato et Kuzumaki

In 1986, Kato and Kuzumaki stated several conjectures in order to give a diophantine characterization of cohomological dimension of fields. In this article, we first prove a local-global principle in this context for number fields. This allows us to give a new proof of one of Kato and Kuzumaki's conjectures for totally imaginary number fields (the first proof was given by Olivier Wittenberg). Our arguments can be generalized to get results for global fields of positive characteristic. We then establish all the conjectures for the fields $\mathbb{C}(x_1,...,x_n)$ and $\mathbb{C}(x_1,...,x_n)((t…

2017-04-03math.AGmath.KTmath.NT

Zéro-cycles sur les espaces homogènes et problème de Galois inverse

Let X be a smooth compactification of a homogeneous space of a linear algebraic group G over a number field k. We establish the conjecture of Colliot-Thélène, Sansuc, Kato and Saito on the image of the Chow group of zero-cycles of X in the product of the same groups over all the completions of k. When G is semisimple and simply connected and the geometric stabiliser is finite and supersolvable, we show that rational points of X are dense in the Brauer-Manin set. For finite supersolvable groups, in particular for finite nilpotent groups, this yields a new proof of Shafarevich's theorem on the i…

2019-10-15math.AGmath.NT

Sur une conjecture de Kato et Kuzumaki concernant les hypersurfaces de Fano

Nous montrons que les corps p-adiques et les corps de nombres totalement imaginaires vérifient la propriété C_1^1 conjecturée par Kato et Kuzumaki en 1986. Autrement dit, si k est l'un de ces corps et f(x_0, ..., x_n) est un polynôme homogène de degré au plus n à coefficients dans k, tout élément de k s'écrit comme produit de normes depuis des extensions finies de k dans lesquelles f admet un zéro non trivial. Nous établissons aussi la conjecture d'Ax sur les corps pseudo-algébriquement clos parfaits pour les corps dont le groupe de Galois absolu est un pro-p-groupe. ----- We prove that p-adic…

2015-05-14math.AGmath.KTmath.NT

Zéro-cycles sur les fibrations au-dessus d'une courbe de genre quelconque

Let X be a smooth and proper variety over a number field k. Conjectures on the image of the Chow group of zero-cycles of X in the product of the corresponding groups over all completions of k were put forward by Colliot-Thélène, Kato and Saito. We prove these conjectures for the total space of fibrations, over curves with finite Tate-Shafarevich group, into rationally connected varieties which satisfy weak approximation, under an abelianness assumption on the singular fibers. ---- Soit X une variété propre et lisse sur un corps de nombres k. Des conjectures sur l'image du groupe de Chow des zé…

2012-05-31math.AGmath.NT