Corpus ID: 233878616

Enumerating algebraic curves and abelian varieties over global function fields with lower order terms

@inproceedings{Han2020EnumeratingAC,
  title={Enumerating algebraic curves and abelian varieties over global function fields with lower order terms},
  author={C. Han and Jun-yong Park},
  year={2020}
}
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. 
1 Citations
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