The local Jacquet-Langlands correspondence via Fourier analysis

Jared Weinstein

Displaying similar documents to “The local Jacquet-Langlands correspondence via Fourier analysis”

Invariants and coinvariants of semilocal units modulo elliptic units

Stéphane Viguié (2012)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $p$ be a prime number, and let $k$ be an imaginary quadratic number field in which $p$ decomposes into two primes $𝔭$ and $\bar{𝔭}$ . Let $k_{\infty}$ be the unique $ℤ_{p}$ -extension of $k$ which is unramified outside of $𝔭$ , and let $K_{\infty}$ be a finite extension of $k_{\infty}$ , abelian over $k$ . Let $𝒰_{\infty} / 𝒞_{\infty}$ be the projective limit of principal semi-local units modulo elliptic units. We prove that the various modules of invariants and coinvariants of $𝒰_{\infty} / 𝒞_{\infty}$ are finite. Our approach uses distributions and the $p$ -adic $L$ -function, as defined in []. ...

Projective representations of generalized symmetric groups.

Morris, Alun O., Jones, Huw I. (2003)

Séminaire Lotharingien de Combinatoire [electronic only]

Similarity:

On a problem of Fell and Doran

Wiesław Żelazko (1991)

Colloquium Mathematicae

Similarity:

Conjugacy classes of series in positive characteristic and Witt vectors.

Sandrine Jean (2009)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $k$ be the algebraic closure of $𝔽_{p}$ and $K$ be the local field of formal power series with coefficients in $k$ . The aim of this paper is the description of the set $𝒴_{n}$ of conjugacy classes of series of order $p^{n}$ for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic $p$ which are invertible and of finite order $p^{n}$ for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series...

On a conjecture of Watkins

Neil Dummigan (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Watkins has conjectured that if $R$ is the rank of the group of rational points of an elliptic curve $E$ over the rationals, then $2^{R}$ divides the modular parametrisation degree. We show, for a certain class of $E$ , chosen to make things as easy as possible, that this divisibility would follow from the statement that a certain $2$ -adic deformation ring is isomorphic to a certain Hecke ring, and is a complete intersection. However, we show also that the method developed by Taylor, Wiles and others,...

Cohomology of integer matrices and local-global divisibility on the torus

Marco Illengo (2008)

Journal de Théorie des Nombres de Bordeaux

Similarity:

Let $p \neq 2$ be a prime and let $G$ be a $p$ -group of matrices in ${SL}_{n} (ℤ)$ , for some integer $n$ . In this paper we show that, when $n < 3 (p - 1)$ , a certain subgroup of the cohomology group $H^{1} (G, 𝔽_{p}^{n})$ is trivial. We also show that this statement can be false when $n \geq 3 (p - 1)$ . Together with a result of Dvornicich and Zannier (see []), we obtain that any algebraic torus of dimension $n < 3 (p - 1)$ enjoys a local-global principle on divisibility by $p$ .