Abelian varieties over finite fields with a specified characteristic polynomial modulo ℓ

Joshua Holden[1]

  • [1] Department of Mathematics Rose-Hulman Institute of Technology Terre Haute, IN 47803, USA

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 1, page 173-178
  • ISSN: 1246-7405

Abstract

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We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P ( T ) modulo ℓ . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order ℓ .

How to cite

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Holden, Joshua. "Abelian varieties over finite fields with a specified characteristic polynomial modulo $\ell $." Journal de Théorie des Nombres de Bordeaux 16.1 (2004): 173-178. <http://eudml.org/doc/249244>.

@article{Holden2004,
abstract = {We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial $P(T)$ modulo $\ell $. As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order $\ell $.},
affiliation = {Department of Mathematics Rose-Hulman Institute of Technology Terre Haute, IN 47803, USA},
author = {Holden, Joshua},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {173-178},
publisher = {Université Bordeaux 1},
title = {Abelian varieties over finite fields with a specified characteristic polynomial modulo $\ell $},
url = {http://eudml.org/doc/249244},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Holden, Joshua
TI - Abelian varieties over finite fields with a specified characteristic polynomial modulo $\ell $
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 1
SP - 173
EP - 178
AB - We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial $P(T)$ modulo $\ell $. As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order $\ell $.
LA - eng
UR - http://eudml.org/doc/249244
ER -

References

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  1. Jeffrey D. Achter and Joshua Holden, Notes on an analogue of the Fontaine-Mazur conjecture. J. Théor. Nombres Bordeaux 15 no.3 (2003), 627–637. Zbl1077.11080MR2142226
  2. Stephen A. DiPippo and Everett W. Howe, Real polynomials with all roots on the unit circle and abelian varieties over finite fields. J. Number Theory 73 (1998), 426–450. Zbl0931.11023MR1657992
  3. Gerhard Frey, Ernst Kani and Helmut Völklein, Curves with infinite K -rational geometric fundamental group. In Helmut Völklein, David Harbater, Peter Müller and J. G. Thompson, editors, Aspects of Galois theory (Gainesville, FL, 1996), volume 256 of London Mathematical Society Lecture Note Series, 85–118. Cambridge Univ. Press, 1999. Zbl0978.14021MR1708603
  4. Joshua Holden, On the Fontaine-Mazur Conjecture for number fields and an analogue for function fields. J. Number Theory 81 (2000), 16–47. Zbl0997.11096MR1743506
  5. Y. Ihara, On unramified extensions of function fields over finite fields. In Y. Ihara, editor, Galois Groups and Their Representations, volume 2 of Adv. Studies in Pure Math. 89–97. North-Holland, 1983. Zbl0542.14011MR732464

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