Results 1 to 10 of about 675,931 (136)
COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP $E_{6}$ [PDF]
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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Density of automorphic points in deformation rings of polarized global Galois representations [PDF]
Duke mathematical journal, 2018 Conjecturally, the Galois representations that are attached to essentially selfdual regular algebraic cuspidal automorphic representations are Zariski-dense in a polarized Galois deformation ring.
Hellmann, Eugen +2 more
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Prismatic $F$-crystals and crystalline Galois representations [PDF]
Cambridge Journal of Mathematics, 2021 Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field. We prove that the category of prismatic $F$-crystals on $\mathcal O_K$ is equivalent to the category of lattices in crystalline $G_K ...
B. Bhatt, P. Scholze
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Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations [PDF]
Journal of the London Mathematical Society, 2022 Let X$X$ be a smooth, separated, geometrically connected scheme defined over a number field K$K$ and {ρλ:π1(X)→GLn(Eλ)}λ$\lbrace \rho _\lambda :\pi _1(X)\rightarrow \mathrm{GL}_n(E_\lambda )\rbrace _\lambda$ a system of semisimple λ$\lambda$ ‐adic ...
Chun Yin Hui
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Rigidity of Automorphic Galois Representations Over CM Fields [PDF]
International mathematics research notices, 2022 We show the vanishing of adjoint Bloch–Kato Selmer groups of automorphic Galois representations over CM fields. This proves their rigidity in the sense that they have no deformations that are de Rham. In order for this to make sense, we also prove that
Lambert A'Campo
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Deformation of Rigid Conjugate Self-dual Galois Representations [PDF]
Acta Mathematica Sinica. English series, 2021 In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain ...
Yi Feng Liu +4 more
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Shimura varieties at level and Galois representations [PDF]
Compositio Mathematica, 2020 We show that the compactly supported cohomology of certain $\text{U}(n,n)$- or $\text{Sp}(2n)$-Shimura varieties with $\unicode[STIX]{x1D6E4}_{1}(p^{\infty })$-level vanishes above the middle degree. The only assumption is that we work over a CM field $F$
A. Caraiani +6 more
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Cohomology of moduli spaces via a result of Chenevier and Lannes [PDF]
Épijournal de Géométrie Algébrique, 2023 We use a classification result of Chenevier and Lannes for algebraic automorphic representations together with a conjectural correspondence with $\ell$-adic absolute Galois representations to determine the Euler characteristics (with values in the ...
Jonas Bergström, Carel Faber
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Seven Small Simple Groups Not Previously Known to Be Galois Over
Mathematics, 2022 In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of ...
Luis Dieulefait +2 more
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Computing mod ℓ Galois representations associated to modular forms for small primes
AIMS Mathematics, 2023 In this paper, we propose an algorithm for computing mod $ \ell $ Galois representations associated to modular forms of weight $ k $ when $ \ell < k-1 $. We also present the corresponding results for the projective Galois representations. Moreover, we
Peng Tian +2 more
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