Results 1 to 10 of about 244 (45)
The Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields
, 2014 Let $K$ be a totally real field. By the asymptotic Fermat's Last Theorem over $K$ we mean the statement that there is a constant $B_K$ such that for prime exponents $p>B_K$ the only solutions to the Fermat equation $a^p + b^p + c^p = 0$ with $a$, $b$, $c$
Freitas, Nuno, Siksek, Samir
core +1 more source
A note on Fontaine theory using different Lubin-Tate groups
, 2013 Using different Lubin-Tate groups, we compare $(\phi, \Gamma)$ modules associated to a Galois representation via Fontaine's ...
Chiarellotto, Bruno R. +1 more
core +1 more source
Filtrations of dc-weak eigenforms
, 2017 The notions of strong, weak and dc-weak eigenforms mod $p^n$ was introduced and studied by Chen, Kiming and Wiese. In this work, we prove that there can be no uniform weight bound (that is, depending only on $p$, $n$) on dc-weak eigenforms mod $p^n$ of ...
Rustom, Nadim
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Cardiac Arrest Induced by Asphyxia Versus Ventricular Fibrillation Elicits Comparable Early Changes in Cytokine Levels in the Rat Brain, Heart, and Serum. [PDF]
J Am Heart Assoc, 2021 Uray T +8 more
europepmc +1 more source
Recovering modular forms and representations from tensor and symmetric powers
, 2004 We consider the problem of determining the relationship between two representations knowing that some tensor or symmetric power of the original represetations coincide.
Rajan, C. S.
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On Fermat's equation over some quadratic imaginary number fields. [PDF]
Res 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
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
Base change for Elliptic Curves over Real Quadratic Fields [PDF]
, 2014 Let E be an elliptic curve over a real quadratic field K and F/K a totally real finite Galois extension. We prove that E/F is modular.Comment: added a short proof of Proposition 2.1 and a few more small changes to improve ...
Dieulefait, Luis, Freitas, Nuno
core +4 more sources
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
Elliptic Curves over Totally Real Cubic Fields are Modular [PDF]
, 2019 We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic curves over real quadratic fields, as well as recent breakthroughs due to
Derickx, Maarten +2 more
core +2 more sources