Support problem for the intermediate Jacobians of l-adic representations

Banaszak, Grzegorz; Gajda, Wojciech; Krasoń, Piotr

doi:10.1016/s0022-314x(02)00122-1

Cited by 21 publications

(43 citation statements)

References 13 publications

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“…[BK], see also [BGK2]). The left (resp., the right) vertical arrow in the diagram (2.1) is an embedding (resp., an isomorphism) for every L (resp., for every w / ∈ S l ).…”

Section: Kummer Theory For L-adic Representationsmentioning

confidence: 99%

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Detecting linear dependence by reduction maps

Banaszak

Gajda

Krasoń

2005

Journal of Number Theory

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“…[BK], see also [BGK2]). The left (resp., the right) vertical arrow in the diagram (2.1) is an embedding (resp., an isomorphism) for every L (resp., for every w / ∈ S l ).…”

Section: Kummer Theory For L-adic Representationsmentioning

confidence: 99%

“…In addition to the methods of the paper [BGK2], we use in the proof of Theorem A the Kummer theory which was developed by Ribet [Ri]. We prove that for Mordell-Weil systems, which come from Tate modules of some abelian varieties A with End(A) = Z and from odd K-groups of number fields, a stronger result than Theorem A holds.…”

Section: Introductionmentioning

confidence: 99%

Detecting linear dependence by reduction maps

Banaszak

Gajda

Krasoń

2005

Journal of Number Theory

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“…The more precise question of Gajda we consider is one possible modification of the support problem for abelian varieties to a non-cyclic setting. The approach we use here is quite different from that of [3] and [1], relying more on the study of the Mordell-Weil group of A as a module for End F A and less on Galois cohomology.…”

Section: Question Let X Y ∈ A(f ) Be Non-torsion Points Suppose Thmentioning

confidence: 99%

Kummer theory of abelian varieties and reductions of Mordell–Weil groups

Weston

2003

Acta Arith.

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“…On the other hand for w / ∈ S l by Lemma 2.8 (3) [BGK2] there is an exact sequence which comes from the restriction-inflation exact sequence…”

Section: Proof Of the Theoremmentioning

confidence: 98%

On reduction map for étale $K$-theory of curves

Banaszak

Gajda

Krasoń

2005

Homology, Homotopy and Applications

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In this paper we investigate reduction of nontorsion elements in theétale K-theory of a curve X over a global field F. We show that the reduction map can be well understood in terms of Galois cohomology of l-adic representations.Dedicated to Victor Snaith on the occasion of his 60-th birthday. IntroductionAssume that X is a smooth, proper and geometrically irreducible curve of genus g, defined over a global field F. Let l be an odd rational prime different from the characteristic of the field F. In the function field case we fix the set of places at infinity. Let n > 0 and let S l be the set of places of F which consists of places of bad reduction of X, places at infinity, and in the number field case, primes lying over l. Denote by X a smooth and proper model of X over the ring of S l -integers of[DF]. For places v ∈S l , we consider the reduction map:induced onétale K-theory by the injection X v → X of the special fiber at v. Theorem . Let J be the Jacobian variety of X and assume that End

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Support problem for the intermediate Jacobians of l-adic representations

Cited by 21 publications

References 13 publications

Detecting linear dependence by reduction maps

Detecting linear dependence by reduction maps

Kummer theory of abelian varieties and reductions of Mordell–Weil groups

On reduction map for étale $K$-theory of curves

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