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2021 | OriginalPaper | Chapter

Restrictions on Weil Polynomials of Jacobians of Hyperelliptic Curves

Authors : Edgar Costa, Ravi Donepudi, Ravi Fernando, Valentijn Karemaker, Caleb Springer, Mckenzie West

Published in: Arithmetic Geometry, Number Theory, and Computation

Publisher: Springer International Publishing

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Inspired by experimental data, we investigate which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by demonstrating that the Weil polynomial of a hyperelliptic Jacobian must have a particular form modulo 2. For fixed g ≥ 1, the proportion of isogeny classes of g-dimensional abelian varieties defined over ?? q $$\mathbb {F}_q$$ which fail this condition is 1 − Q(2g + 2)∕2g as q →∞ ranges over odd prime powers, where Q(n) denotes the number of partitions of n into odd parts.

Metadata
Title
Restrictions on Weil Polynomials of Jacobians of Hyperelliptic Curves
Authors
Edgar Costa
Ravi Donepudi
Ravi Fernando
Valentijn Karemaker
Caleb Springer
Mckenzie West
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-80914-0_7

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