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arXiv · 2601.18557

Arithmetic volumes of moduli stacks of Shtukas

Tony Feng·Zhiwei Yun·Wei Zhang
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Abstract

We define and study "tautological classes" in the cohomology of moduli stacks of shtukas, pursuing two directions of applications. First, we prove a formula relating the "arithmetic volume" of tautological classes to higher derivatives of Artin $L$-functions, which can be viewed as an arithmetic analog of Hirzebruch's Proportionality principle. Second, we define and analyze the structure of the "phantom tautological ring", using a general relation between Hecke correspondences and Vinberg's degeneration, and give applications to a function field analog of Colmez's Conjecture.

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Tony Feng, Zhiwei Yun, Wei Zhang. 2026-01-26. Arithmetic volumes of moduli stacks of Shtukas. https://arxiv.org/abs/2601.18557

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