Results 1 to 10 of about 278 (30)

On Fermat's equation over some quadratic imaginary number fields. [PDF]

open access: yesRes Number Theory, 2018
Assuming a deep but standard conjecture in the Langlands programme, we prove Fermat's Last Theorem over $\mathbb Q(i)$. Under the same assumption, we also prove that, for all prime exponents $p \geq 5$, Fermat's equation $a^p+b^p+c^p=0$ does not have non-
Ţurcaş GC.
europepmc   +4 more sources

ON THE INTEGRAL HODGE AND TATE CONJECTURES OVER A NUMBER FIELD

open access: yesForum 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

THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$

open access: yesForum 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

Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case

open access: yesForum 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

COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP $E_{6}$

open access: yesForum 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
doaj   +1 more source

SERRE WEIGHTS AND WILD RAMIFICATION IN TWO-DIMENSIONAL GALOIS REPRESENTATIONS

open access: yesForum 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
doaj   +1 more source

UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES

open access: yesForum of Mathematics, Sigma, 2017
Let $p$ be a prime number and $F$ a totally real number ...
MATTHEW EMERTON   +2 more
doaj   +1 more source

COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES

open access: yesForum of Mathematics, Sigma, 2016
Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
doaj   +1 more source

Cardiac Arrest Induced by Asphyxia Versus Ventricular Fibrillation Elicits Comparable Early Changes in Cytokine Levels in the Rat Brain, Heart, and Serum. [PDF]

open access: yesJ Am Heart Assoc, 2021
Uray T   +8 more
europepmc   +1 more source

Heegner points in Coleman families

open access: yesProceedings 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

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