Results 11 to 20 of about 53 (53)
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
DERIVED HECKE ALGEBRA AND COHOMOLOGY OF ARITHMETIC GROUPS
Forum of Mathematics, Pi, 2019 We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\unicode[STIX]{x1D6E4}$.
AKSHAY VENKATESH
doaj +1 more source
On local Galois deformation rings: generalised tori
Forum of Mathematics, SigmaWe 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
ON THE INTEGRAL HODGE AND TATE CONJECTURES OVER A NUMBER FIELD
Forum of Mathematics, Sigma, 2013 Hassett and Tschinkel gave counterexamples to the integral Hodge conjecture among 3-folds over a number field. We work out their method in detail, showing that essentially all known counterexamples to the integral Hodge conjecture over the complex ...
BURT TOTARO
doaj +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