• Corpus ID: 235743197

Level structure, arithmetic representations, and noncommutative Siegel linearization

@inproceedings{Kadets2021LevelSA,
  title={Level structure, arithmetic representations, and noncommutative Siegel linearization},
  author={Borys Kadets and Daniel Litt},
  year={2021}
}
. Let ℓ be a prime, k a finitely generated field of characteristic different from ℓ , and X a smooth geometrically connected curve over k . Say a semisimple representation of π ´et1 ( X ¯ k ) is arithmetic if it extends to a finite index subgroup of π ´et1 ( X ). We show that there exists an effective constant N = N ( X,ℓ ) such that any semisimple arithmetic representation of π ´et1 ( X ¯ k ) into GL n ( Z ℓ ), which is trivial mod ℓ N , is in fact trivial. This extends a previous result of the… 

References

SHOWING 1-10 OF 16 REFERENCES
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
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
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
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
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
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
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
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
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
Linear forms in p-adic logarithms
...
1
2
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