An ordinary rank-two case of local-global compatibility for automorphic representations of arbitrary weight over CM fields [PDF]
Mathematical Research Letters, 2021 We prove a rank-two potential automorphy theorem for mod $l$ representations satisfying an ordinary condition. Combined with an ordinary automorphy lifting theorem, we prove a rank-two, $p \ne l$ case of local-global compatibility for regular algebraic ...
Yujie Yang
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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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On counting cuspidal automorphic representations for GSp(4) [PDF]
Forum mathematicum, 2020 We find the number sk(p,Ω)s_{k}(p,\Omega) of cuspidal automorphic representations of GSp(4,AQ)\mathrm{GSp}(4,\mathbb{A}_{\mathbb{Q}}) with trivial central character such that the archimedean component is a holomorphic discrete series representation of ...
Manami Roy, Ralf Schmidt, Shaoyun Yi
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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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On the vanishing of adjoint Bloch–Kato Selmer groups of irreducible automorphic Galois representations [PDF]
Pure and Applied Mathematics Quarterly, 2022 Let $\rho$ be the $p$-adic Galois representation attached to a cuspidal, regular algebraic, polarizable automorphic representation of $GL_n$. Assuming only that $\rho$ satisfies an irreducibility condition, we prove the vanishing of the adjoint Bloch ...
J. Thorne
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Chow groups and L-derivatives of automorphic motives for unitary groups, II.
Forum of Mathematics, Pi, 2022 In this article, we improve our main results from [LL21] in two directions: First, we allow ramified places in the CM extension $E/F$ at which we consider representations that are spherical with respect to a certain special maximal compact subgroup, by ...
Chao Li, Yifeng Liu
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An Automorphic Distance Metric and Its Application to Node Embedding for Role Mining
Complexity, 2021 Role is a fundamental concept in the analysis of the behavior and function of interacting entities in complex networks. Role discovery is the task of uncovering the hidden roles of nodes within a network.
Víctor Martínez +2 more
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Sato–Tate equidistribution for families of automorphic representations through the stable trace formula [PDF]
Algebra & Number Theory, 2019 In arXiv:1208.1945, Shin and Templier proved certain equidistribution bounds on local components of certain families of automorphic representations. We extend their weight-aspect results to families of automorphic representations where the Archimedean ...
Rahul Dalal
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RAISING THE LEVEL OF AUTOMORPHIC REPRESENTATIONS OF $\mathrm {GL}_{2n}$ OF UNITARY TYPE [PDF]
Journal of the Institute of Mathematics of Jussieu, 2019 We use the endoscopic classification of automorphic representations of even-dimensional unitary groups to construct level-raising congruences.
Christos Anastassiades, J. Thorne
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