Results 11 to 20 of about 55 (55)
Heegner points in Coleman families
Proceedings of the London Mathematical Society, Volume 122, Issue 1, Page 124-152, January 2021., 2021 Abstract We construct two‐parameter analytic families of Galois cohomology classes interpolating the étale Abel–Jacobi images of generalised Heegner cycles, with both the modular form and Grössencharacter varying in p‐adic families.
Dimitar Jetchev +2 more
wiley +1 more source
Twist‐minimal trace formulas and the Selberg eigenvalue conjecture
Journal of the London Mathematical Society, Volume 102, Issue 3, Page 1067-1134, December 2020., 2020 Abstract We derive a fully explicit version of the Selberg trace formula for twist‐minimal Maass forms of weight 0 and arbitrary conductor and nebentypus character, and apply it to prove two theorems. First, conditional on Artin's conjecture, we classify the even 2‐dimensional Artin representations of small conductor; in particular, we show that the ...
Andrew R. Booker +2 more
wiley +1 more source
On a variation of the Erdős–Selfridge superelliptic curve
Bulletin of the London Mathematical Society, Volume 51, Issue 4, Page 633-638, August 2019., 2019 Abstract In a recent paper by Das, Laishram and Saradha, it was shown that if there exists a rational solution of yl=(x+1)…(x+i−1)(x+i+1)…(x+k) for i not too close to k/2 and y≠0, then logl<3k. In this paper, we extend the number of terms that can be missing in the equation and remove the condition on i.
Sam Edis
wiley +1 more source
Locally analytic vectors and decompletion in mixed characteristic
Forum of Mathematics, SigmaIn p-adic Hodge theory and the p-adic Langlands program, Banach spaces with $\mathbf {Q}_p$ -coefficients and p-adic Lie group actions are central.
Gal Porat
doaj +1 more source
THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$
Forum of Mathematics, Pi, 2015 Let $p>2$ be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate representations, over arbitrary finite extensions of $\mathbb{Q}_{p}$.
TOBY GEE, TONG LIU, DAVID SAVITT
doaj +1 more source
Vanishing theorems for the mod p cohomology of some simple Shimura varieties
Forum of Mathematics, Sigma, 2020 We show that the mod p cohomology of a simple Shimura variety treated in Harris-Taylor’s book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we show the vanishing
Teruhisa Koshikawa
doaj +1 more source
EULER SYSTEMS FOR HILBERT MODULAR SURFACES
Forum of Mathematics, Sigma, 2018 We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular surfaces.
ANTONIO LEI +2 more
doaj +1 more source
Smith theory and cyclic base change functoriality
Forum of Mathematics, PiLafforgue and Genestier-Lafforgue have constructed the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields.
Tony Feng
doaj +1 more source
The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms
Forum of Mathematics, PiWe prove the Ramanujan and Sato–Tate conjectures for Bianchi modular forms of weight at least $2$ . More generally, we prove these conjectures for all regular algebraic cuspidal automorphic representations of $\operatorname {\mathrm {GL}}_2 ...
George Boxer +4 more
doaj +1 more source
Forum of Mathematics, Sigma, 2014 We extend the modularity lifting result of P. Kassaei (‘Modularity lifting in parallel weight one’,J. Amer. Math. Soc. 26 (1) (2013), 199–225) to allow Galois representations with some ramification at
PAYMAN L. KASSAEI +2 more
doaj +1 more source