Results 21 to 30 of about 245 (47)
Rational points on Erdős–Selfridge superelliptic curves [PDF]
, 2015 Given k⩾2k⩾2, we show that there are at most finitely many rational numbers xx and y≠0y≠0 and integers ℓ⩾2ℓ⩾2 (with (k,ℓ)≠(2,2)(k,ℓ)≠(2,2)) for which $$\begin{eqnarray}x(x+1)\cdots (x+k-1)=y^{\ell }.\end{eqnarray}$$ In particular, if we assume that ℓℓ is
Darmon +6 more
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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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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
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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
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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
core
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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Partial Hasse invariants on splitting models of Hilbert modular varieties [PDF]
, 2016 Let $F$ be a totally real field of degree $g$, and let $p$ be a prime number. We construct $g$ partial Hasse invariants on the characteristic $p$ fiber of the Pappas-Rapoport splitting model of the Hilbert modular variety for $F$ with level prime to $p$,
Reduzzi, Davide A., Xiao, Liang
core
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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The passivity of lithium electrodes in liquid electrolytes for secondary batteries
Nature Reviews Materials, 2021Dominic Bresser +2 more
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