Results 11 to 20 of about 283 (24)
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
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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
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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
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COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP $E_{6}$
Forum of Mathematics, Sigma, 2019 We construct, over any CM field, compatible systems of $l$-adic Galois representations that appear in the cohomology of algebraic varieties and have (for all $l$) algebraic monodromy groups equal to the exceptional group of type $E_{6}$.
GEORGE BOXER +5 more
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SERRE WEIGHTS AND WILD RAMIFICATION IN TWO-DIMENSIONAL GALOIS REPRESENTATIONS
Forum of Mathematics, Sigma, 2016 A generalization of Serre’s Conjecture asserts that if $F$ is a totally real field, then certain characteristic
LASSINA DEMBÉLÉ +2 more
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UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES
Forum of Mathematics, Sigma, 2017 Let $p$ be a prime number and $F$ a totally real number ...
MATTHEW EMERTON +2 more
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COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
Forum of Mathematics, Sigma, 2016 Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
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Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4
, 2018 We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve ...
Kiming, Ian, Rustom, Nadim
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Elliptic curves with maximal Galois action on their torsion points
, 2008 Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, \rho_E : Gal(\bar{k}/k) \to GL_2(\hat{Z}).
Zywina, David
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Abelian varieties over large algebraic fields with infinite torsion [PDF]
, 2010 Let A be an abelian variety of positive dimension defined over a number field K and let Kbar be a fixed algebraic closure of K. For each element sigma of the absolute Galois group Gal(Kbar/K), let Kbar(sigma) be the fixed field of sigma in Kbar. We shall
Zywina, David
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