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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyperelliptic curves over $\mathbb {F}_2$ of every $2$-rank without extra automorphisms
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by Hui June Zhu PDF
Proc. Amer. Math. Soc. 134 (2006), 323-331 Request permission

Abstract:

We prove that for any pair of integers $0\leq r\leq g$ such that $g\geq 3$ or $r>0$, there exists a (hyper)elliptic curve $C$ over $\mathbb {F}_2$ of genus $g$ and $2$-rank $r$ whose automorphism group consists of only identity and the (hyper)elliptic involution. As an application, we prove the existence of principally polarized abelian varieties $(A,\lambda )$ over $\mathbb {F}_2$ of dimension $g$ and $2$-rank $r$ such that $\operatorname {Aut}(A,\lambda )=\{\pm 1\}$.
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Additional Information
  • Hui June Zhu
  • Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
  • Email: zhu@cal.berkeley.edu
  • Received by editor(s): July 20, 2004
  • Published electronically: August 25, 2005
  • Communicated by: David E. Rohrlich
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 323-331
  • MSC (2000): Primary 11G10, 14G15
  • DOI: https://doi.org/10.1090/S0002-9939-05-08294-8
  • MathSciNet review: 2175998