Geometric Manin's conjecture in characteristic $p$

Brian Lehmann; Sho Tanimoto

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arXiv · 2601.09227

Geometric Manin's conjecture in characteristic $p$

Brian Lehmann·Sho Tanimoto

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Abstract

Geometric Manin's conjecture for complex Fano varieties describes the structure of the moduli space of curves. We propose a version of this conjecture in characteristic $p$ and describe its connection to the Batyrev--Manin--Peyre--Tschinkel conjecture over global fields. This is a survey paper written for a volume of the Summer Research Institute in Algebraic Geometry held at Colorado State University in 2025.

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Brian Lehmann, Sho Tanimoto. 2026-01-14. Geometric Manin's conjecture in characteristic $p$. https://arxiv.org/abs/2601.09227

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