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Lifting and automorphy of reducible mod p Galois representations over global fields

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0 Published in 2021 at "Inventiones mathematicae"

DOI: 10.1007/s00222-021-01085-7

Abstract: We extend the lifting methods of our previous paper to lift reducible odd representations $\bar{\rho}:\mathrm{Gal}(\overline{F}/F) \to G(k)$ of Galois groups of global fields $F$ valued in Chevalley groups $G(k)$. Lifting results, when combined with automorphy… read more here.

Keywords: global fields; galois; mod galois; galois representations ... See more keywords

Reductions of Galois representations of slope 1

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1 Published in 2018 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2018.04.023

Abstract: Abstract We compute the reductions of irreducible crystalline two-dimensional representations of G Q p of slope 1, for primes p ≥ 5 , and all weights. We describe the semisimplification of the reductions completely. In… read more here.

Keywords: representations slope; galois representations; reductions galois;

Local universal lifting spaces of mod l Galois representations

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1 Published in 2017 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2016.12.006

Abstract: Abstract Let p and l be distinct primes, K a finite extension of Q p , and ρ ‾ : Gal ( K ‾ / K ) → GL n ( F ‾ l )… read more here.

Keywords: lifting spaces; universal lifting; spaces mod; mod galois ... See more keywords

UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES

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0 Published in 2017 at "Forum of Mathematics, Sigma"

DOI: 10.1017/fms.2017.26

Abstract: Let $p$ be a prime number and $F$ a totally real number field. For each prime $\mathfrak{p}$ of $F$ above $p$ we construct a Hecke operator $T_{\mathfrak{p}}$ acting on $(\text{mod}\,p^{m})$ Katz Hilbert modular classes which… read more here.

Keywords: unramifiedness galois; arising hilbert; galois representations; hilbert modular ... See more keywords

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

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0 Published in 2019 at "Forum of Mathematics, Sigma"

DOI: 10.1017/fms.2018.24

Abstract: 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… read more here.

Keywords: compatible systems; representations associated; galois representations; exceptional group ... See more keywords

LIFTING N-DIMENSIONAL GALOIS REPRESENTATIONS TO CHARACTERISTIC ZERO

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0 Published in 2018 at "Glasgow Mathematical Journal"

DOI: 10.1017/s0017089518000149

Abstract: Abstract Let F be a number field, let N ≥ 3 be an integer, and let k be a finite field of characteristic ℓ. We show that if ρ:GF → GLN(k) is a continuous representation… read more here.

Keywords: dimensional galois; representations characteristic; galois representations; lifting dimensional ... See more keywords

Rigidity of Automorphic Galois Representations Over CM Fields

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1 Published in 2022 at "International Mathematics Research Notices"

DOI: 10.1093/imrn/rnad087

Abstract: 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… read more here.

Keywords: automorphic galois; galois representations; representations fields; rigidity automorphic ... See more keywords

On some p‐adic Galois representations and form class groups

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2 Published in 2022 at "Mathematika"

DOI: 10.1112/mtk.12141

Abstract: Let K be an imaginary quadratic field of discriminant dK$d_K$ with ring of integers OK$\mathcal {O}_K$ . When K is different from Q(−1)$\mathbb {Q}(\sqrt {-1})$ and Q(−3)$\mathbb {Q}(\sqrt {-3})$ , we consider a specific elliptic… read more here.

Keywords: field; form class; mathbb; class ... See more keywords

Shimura varieties at level $\unicode[STIX]{x1D6E4}_{1}(p^{\infty })$ and Galois representations

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1 Published in 2020 at "Compositio Mathematica"

DOI: 10.1112/s0010437x20007149

Abstract: 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 $F$ in which… read more here.

Keywords: x1d6e4 infty; shimura varieties; stix x1d6e4; unicode stix ... See more keywords

Deformations of reducible Galois representations to Hida-families

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0 Published in 2021 at "International Journal of Number Theory"

DOI: 10.1142/s1793042122500087

Abstract: The global deformation theory of residually reducible Galois representations with fixed auxiliary conditions is studied. We show that [Formula: see text] lifts to a Hida line for which the weights range over a congruence class… read more here.

Keywords: reducible galois; formula see; galois representations; see text ... See more keywords