Level structure, arithmetic representations, and noncommutative Siegel linearization

@article{Kadets2022LevelSA,
  title={Level structure, arithmetic representations, and noncommutative Siegel linearization},
  author={Borys Kadets and Daniel Litt},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  year={2022},
  volume={2022},
  pages={219 - 238}
}
  • Borys Kadets, Daniel Litt
  • Published 5 July 2021
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract Let ℓ{\ell} be a prime, k a finitely generated field of characteristic different from ℓ{\ell}, and X a smooth geometrically connected curve over k. Say a semisimple representation of π1ét⁢(Xk¯){\pi_{1}^{{\text{\'{e}t}}}(X_{\bar{k}})} is arithmetic if it extends to a finite index subgroup of π1ét⁢(X){\pi_{1}^{{\text{\'{e}t}}}(X)}. We show that there exists an effective constant N=N⁢(X,ℓ){N=N(X,\ell)} such that any semisimple arithmetic representation of π1ét⁢(Xk¯){\pi_{1}^{{\text{\'{e}t… 

References

SHOWING 1-10 OF 16 REFERENCES
Arithmetic representations of fundamental groups I
Let X be a normal algebraic variety over a finitely generated field k of characteristic zero, and let $$\ell $$ℓ be a prime. Say that a continuous $$\ell $$ℓ-adic representation $$\rho $$ρ of $$\pi
Arithmetic representations of fundamental groups, II: Finiteness
Let $X$ be a smooth curve over a finitely generated field $k$, and let $\ell$ be a prime different from the characteristic of $k$. We analyze the dynamics of the Galois action on the deformation
P-torsion monodromy representations of elliptic curves over geometric function fields
Given a complex quasiprojective curve $B$ and a non-isotrivial family $\mathcal{E}$ of elliptic curves over $B$, the $p$-torsion $\mathcal{E}[p]$ yields a monodromy representation
Uniform boundedness of level structures on abelian varieties over complex function fields
Let X = Ω/Γ be a smooth quotient of a bounded symmetric domain Ω by an arithmetic subgroup . We prove the following generalization of Nadel's result: for any non-negative integer g, there exists a
The geometric torsion conjecture for abelian varieties with real multiplication
The geometric torsion conjecture asserts that the torsion part of the Mordell--Weil group of a family of abelian varieties over a complex quasiprojective curve is uniformly bounded in terms of the
The nonexistence of certain level structures on abelian varieties over complex function fields
Let A be a principally polarized abelian variety of dimension g over a number field k. The Mordell-Weil theorem tells us that the group A(k) of k-rational points of A is finitely generated; in
Chow's K/k-image and K/k-trace, and the Lang-Neron theorem
Let K/k be an extension of fields, and assume that it is primary: the algebraic closure of k in K is purely inseparable over k. The most interesting case in practice is when K/k is a regular
Étale cohomology of rank one $$\ell $$-adic local systems in positive characteristic
We show that in positive characteristic special loci of deformation spaces of rank one $\ell$-adic local systems are quasilinear. From this we deduce the Hard Lefschetz theorem for rank one
Chtoucas de Drinfeld et correspondance de Langlands
Résumé.On démontre la correspondance de Langlands pour GLr sur les corps de fonctions. La preuve généralise celle de Drinfeld en rang 2 : elle consiste à réaliser la correspondance en rang r dans la
Linear forms in p-adic logarithms
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