Notes on an analogue of the Fontaine-Mazur conjecture

Jeffrey D. Achter; Joshua Holden

Displaying similar documents to “Notes on an analogue of the Fontaine-Mazur conjecture”

On the conjectures of Birch and Swinnerton-Dyer and a geometric analog

John Tate (1964-1966)

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Curves and their fundamental groups

Gerd Faltings (1997-1998)

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Problems from the workshop on Automorphisms of Curves (Leiden, August, 2004)

Gunther Cornelissen, Frans Oort (2005)

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In the week of August, 16th-20th of 2004, we organized a workshop about “Automorphisms of Curves” at the Lorentz Center in Leiden. The programme included two “problem sessions”. Some of the problems presented at the workshop were written down; this is our edition of these refereed and revised papers. Edited by Gunther Cornelissen and Frans Oort with contributions of I. Bouw; T. Chinburg; G. Cornelissen; C. Gasbarri; D. Glass; C. Lehr; M. Matignon; F. Oort; R. Pries; S. Wewers. ...

Galois theory and torsion points on curves

Matthew H. Baker, Kenneth A. Ribet (2003)

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In this paper, we survey some Galois-theoretic techniques for studying torsion points on curves. In particular, we give new proofs of some results of A. Tamagawa and the present authors for studying torsion points on curves with “ordinary good” or “ordinary semistable” reduction at a given prime. We also give new proofs of : (1) the Manin-Mumford conjecture : there are only finitely many torsion points lying on a curve of genus at least $2$ embedded in its jacobian by an Albanese map;...

On a theorem of Tate

Fedor Bogomolov, Yuri Tschinkel (2008)

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We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.

Semistable reduction and torsion subgroups of abelian varieties

Alice Silverberg, Yuri G. Zarhin (1995)

Annales de l'institut Fourier

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The main result of this paper implies that if an abelian variety over a field $F$ has a maximal isotropic subgroup of $n$ -torsion points all of which are defined over $F$ , and $n \geq 5$ , then the abelian variety has semistable reduction away from $n$ . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its $n$ -torsion points are defined over a field $F$ and $n \geq 3$ , then the abelian variety has semistable reduction away from $n$ . We also give information about the Néron...

Rational torsion points on elliptic curves over number fields

Bas Edixhoven (1993-1994)

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Lang’s conjecture in characteristic $p$ : an explicit bound

Alexandru Buium, José Felipe Voloch (1996)

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Refined theorems of the Birch and Swinnerton-Dyer type

Ki-Seng Tan (1995)

Annales de l'institut Fourier

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In this paper, we generalize the context of the Mazur-Tate conjecture and sharpen, in a certain way, the statement of the conjecture. Our main result will be to establish the truth of a part of these new sharpened conjectures, provided that one assume the truth of the classical Birch and Swinnerton-Dyer conjectures. This is particularly striking in the function field case, where these results can be viewed as being a refinement of the earlier work of Tate and Milne.