Results 11 to 20 of about 282 (32)

On local Galois deformation rings: generalised tori

Forum of Mathematics, Sigma
We study deformation theory of mod p Galois representations of p-adic fields with values in generalised tori, such as L-groups of (possibly non-split) tori.
Vytautas Paškūnas, Julian Quast
doaj   +1 more source

Cuspidal ${\ell }$ -modular representations of $\operatorname {GL}_n({ F})$ distinguished by a Galois involution

Forum of Mathematics, Sigma
Let ${ F}/{ F}_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq 2$ with Galois automorphism $\sigma $ , and let R be an algebraically closed field of characteristic $\ell ...
Robert Kurinczuk, Nadir Matringe, Vincent Sécherre   +2 more
doaj   +1 more source

"Divergent" Ramanujan-type supercongruences

, 2010
"Divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases.
Guillera, Jesús, Zudilin, Wadim
core   +2 more sources

Arithmetic properties of Fredholm series for p-adic modular forms [PDF]

, 2016
We study the relationship between recent conjectures on slopes of overconvergent p-adic modular forms "near the boundary" of p-adic weight space. We also prove in tame level 1 that the coefficients of the Fredholm series of the U_p operator never vanish ...
Bergdall, John, Pollack, Robert
core   +3 more sources

Modularity of trianguline Galois representations

Forum of Mathematics, Sigma
We use the theory of trianguline $(\varphi ,\Gamma )$ -modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at p, including those with characteristic p coefficients.
Rebecca Bellovin
doaj   +1 more source

Stability in the category of smooth mod-p representations of ${\mathrm {SL}}_2(\mathbb {Q}_p)$

Forum of Mathematics, Sigma
Let $p \geq 5$ be a prime number, and let $G = {\mathrm {SL}}_2(\mathbb {Q}_p)$ . Let $\Xi = {\mathrm {Spec}}(Z)$ denote the spectrum of the centre Z of the pro-p Iwahori–Hecke algebra of G with coefficients in a field k of ...
Konstantin Ardakov, Peter Schneider
doaj   +1 more source

Quasi-polynomial representations of double affine Hecke algebras

Forum of Mathematics, Sigma
We introduce an explicit family of representations of the double affine Hecke algebra $\mathbb {H}$ acting on spaces of quasi-polynomials, defined in terms of truncated Demazure-Lusztig type operators.
Siddhartha Sahi, Jasper Stokman, Vidya Venkateswaran   +2 more
doaj   +1 more source

A remark on non-integral -adic slopes for modular forms [PDF]

, 2017
We give a sufficient condition, namely “Buzzard irregularity”, for there to exist a cuspidal eigenform which does not have integral -adic slope.Accepted ...
Bergdall, John, Pollack, R.
core  

Curvature on the integers, I

, 2015
Starting with a symmetric/antisymmetric matrix with integer coefficients (which we view as an analogue of a metric/form on a principal bundle over the "manifold" Spec Z) we introduce arithmetic analogues of Chern connections and their curvature (in which
Barrett, Malik, Buium, Alexandru
core   +1 more source

Slopes of modular forms and the ghost conjecture [PDF]

, 2017
We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on classical slopes and more recent conjectures on slopes "at the boundary of ...
Bergdall, John, Pollack, Robert
core   +7 more sources