Arithmetic volumes of moduli stacks of Shtukas
Number Theory
2026-01-27 v1 Algebraic Geometry
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 -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.
Keywords
Cite
@article{arxiv.2601.18557,
title = {Arithmetic volumes of moduli stacks of Shtukas},
author = {Tony Feng and Zhiwei Yun and Wei Zhang},
journal= {arXiv preprint arXiv:2601.18557},
year = {2026}
}