Notes on an analogue of the Fontaine-Mazur conjecture

Jeffrey D. Achter; Joshua Holden

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 3, page 627-637
  • ISSN: 1246-7405

Abstract

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We estimate the proportion of function fields satisfying certain conditions which imply a function field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even jacobians) over a finite field which have a rational point of order ℓ .

How to cite

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Achter, Jeffrey D., and Holden, Joshua. "Notes on an analogue of the Fontaine-Mazur conjecture." Journal de théorie des nombres de Bordeaux 15.3 (2003): 627-637. <http://eudml.org/doc/249110>.

@article{Achter2003,
abstract = {We estimate the proportion of function fields satisfying certain conditions which imply a function field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even jacobians) over a finite field which have a rational point of order $\ell $.},
author = {Achter, Jeffrey D., Holden, Joshua},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {uniformly powerful pro- group; Equidistribution},
language = {eng},
number = {3},
pages = {627-637},
publisher = {Université Bordeaux I},
title = {Notes on an analogue of the Fontaine-Mazur conjecture},
url = {http://eudml.org/doc/249110},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Achter, Jeffrey D.
AU - Holden, Joshua
TI - Notes on an analogue of the Fontaine-Mazur conjecture
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 3
SP - 627
EP - 637
AB - We estimate the proportion of function fields satisfying certain conditions which imply a function field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even jacobians) over a finite field which have a rational point of order $\ell $.
LA - eng
KW - uniformly powerful pro- group; Equidistribution
UR - http://eudml.org/doc/249110
ER -

References

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  10. [10] J. Holden, On the Fontaine-Mazur Conjecture for number fields and an analogue for function fields. J. Number Theory81 (2000), 16-47. Zbl0997.11096MR1743506
  11. [11] Y. Ihara, On unramified extensions of function fields over finite fields. Y. Ihara, editor, Galois Groups and Their Representations, Adv. Studies in Pure Math.2 (1983), 89-97. Zbl0542.14011MR732464
  12. [12] N.M. Katz, P. Sarnak, Random matrices, Frobenius eigenvalues, and monodromy. American Mathematical Society, 1999. Zbl0958.11004MR1659828

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