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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

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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.

Title
Restrictions on Weil Polynomials of Jacobians of Hyperelliptic Curves
Authors
Edgar Costa
Ravi Donepudi
Ravi Fernando
Valentijn Karemaker
Caleb Springer
Mckenzie West