Lifting and automorphy of reducible mod p Galois representations over global fields
Sign Up to like & getrecommendations! 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
Numerical Computation of Galois Groups
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DOI: 10.1007/s10208-017-9356-x
Abstract: The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. We give numerical methods to compute the Galois group and study it when… read more here.
Keywords: numerical computation; galois; group; galois groups ... See more keywords
Reduced group schemes as iterative differential Galois groups
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DOI: 10.1007/s11856-020-2019-7
Abstract: This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative… read more here.
Keywords: schemes iterative; iterative differential; reduced group; galois ... See more keywords
Hopf Galois structures on separable field extensions of odd prime power degree
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DOI: 10.1016/j.jalgebra.2018.11.004
Abstract: A Hopf Galois structure on a finite field extension $L/K$ is a pair $(\mathcal{H},\mu)$, where $\mathcal{H}$ is a finite cocommutative $K$-Hopf algebra and $\mu$ a Hopf action. In this paper, we present several results on… read more here.
Keywords: field; extension; galois structures; hopf galois ... See more keywords
Lübeck's classification of representations of finite simple groups of Lie type and the inverse Galois problem for some orthogonal groups
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DOI: 10.1016/j.jnt.2019.06.010
Abstract: Abstract In this paper we prove that for each integer of the form n = 4 ϖ (where ϖ is a prime between 17 and 73) at least one of the following groups: P Ω… read more here.
Keywords: groups lie; simple groups; galois; lie type ... See more keywords
Constructing certain special analytic Galois extensions
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DOI: 10.1016/j.jnt.2019.10.023
Abstract: Abstract For every prime p ≥ 5 for which a certain condition on the class group Cl ( Q ( μ p ) ) is satisfied, we construct a p-adic analytic Galois extension of the… read more here.
Keywords: constructing certain; galois extensions; certain special; analytic galois ... See more keywords
REFINED SWAN CONDUCTORS $\text{mod}~p$ OF ONE-DIMENSIONAL GALOIS REPRESENTATIONS
Sign Up to like & getrecommendations! Published in 2019 at "Nagoya Mathematical Journal"
DOI: 10.1017/nmj.2019.13
Abstract: For a character of the absolute Galois group of a complete discrete valuation field, we define a lifting of the refined Swan conductor, using higher dimensional class field theory. read more here.
Keywords: text mod; conductors text; galois; swan conductors ... See more keywords
Decomposing Jacobians Via Galois covers
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DOI: 10.1080/10586458.2021.1926008
Abstract: Let φ : X → Y be a (possibly ramied) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of φ, up to isogeny, as the Jacobian… read more here.
Keywords: decomposing jacobians; galois covers; galois; jacobians via ... See more keywords
One-Relator Maximal Pro-p Galois Groups and the Koszulity Conjectures
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DOI: 10.1093/qmath/haaa049
Abstract: Let $p$ be a prime number and let ${K}$ be a field containing a root of 1 of order $p$. If the absolute Galois group $G_{K}$ satisfies $\dim H^1(G_{K},\mathbb{F}_p) read more here.
Keywords: relator maximal; one relator; koszulity conjectures; galois ... See more keywords
Shimura varieties at level $\unicode[STIX]{x1D6E4}_{1}(p^{\infty })$ and Galois representations
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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
A Morita-Takeuchi Context and Hopf Coquasigroup Galois Coextensions
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DOI: 10.3390/sym15020551
Abstract: For H a Hopf quasigroup and C, a left quasi H-comodule coalgebra, we show that the smash coproduct C⋊H (as a symmetry of smash product) is linked to some quotient coalgebra Q=C/CH*+ by a Morita-Takeuchi… read more here.
Keywords: morita takeuchi; galois; symmetry; takeuchi context ... See more keywords