@inbook{1930960c123c4447a9a21ab91b3ad8ae,

title = "Restrictions on Weil polynomials of Jacobians of hyperelliptic curves",

abstract = " Inspired by experimental data, this paper investigates 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 ${g\geq1}$, the proportion of isogeny classes of $g$ dimensional abelian varieties defined over $\mathbb{F}_q$ which fail this condition is $1 - Q(2g + 2)/2^g$ as $q\to\infty$ ranges over odd prime powers, where $Q(n)$ denotes the number of partitions of $n$ into odd parts. ",

author = "Edgar Costa and Ravi Donepudi and Ravi Fernando and Valentijn Karemaker and Caleb Springer and Mckenzie West",

note = "15 pages, 1 figure. To appear in the Simons Symposia proceedings volume for the Simons Collaboration {"}Arithmetic Geometry, Number Theory and Computation{"}",

year = "2022",

doi = "10.1007/978-3-030-80914-0_7",

language = "English",

isbn = "978-3-030-80913-3",

series = "Simons Symposia",

publisher = "Springer",

pages = "259–276",

editor = "Balakrishnan, {Jennifer S. } and Elkies, {Noam } and Hassett, {Brendan } and Poonen, {Bjorn } and Sutherland, {Andrew } and Voight, {John }",

booktitle = "Arithmetic Geometry, Number Theory, and Computation",

address = "Germany",

edition = "1",

}