Enumerating algebraic curves and abelian varieties over global function fields with lower order terms
Abstract
Given asymptotic counts in number theory, a question of Venkatesh asks what is the topological nature of lower order terms. We consider the arithmetic aspect of the inertia stack of an algebraic stack over finite fields to partially answer this question. Subsequently, we enumerate algebraic curves and abelian varieties with precise lower order terms ordered by bounded discriminant height over $\mathbb{F}_q(t)$ which renders new heuristics over $\mathbb{Q}$ through the global fields analogy.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.00563
 Bibcode:
 2020arXiv200200563H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  Number Theory
 EPrint:
 43 pages. Added the arithmetic geometry of inertia stacks of algebraic stacks and its connection to lower order terms of enumerations. The Appendix (reinforced by Changho Han) has been integrated from arXiv:2002.06527. Comments welcome!