Arithmetic volumes of moduli stacks of Shtukas
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912849855512576 |
|---|---|
| author | Feng, Tony Yun, Zhiwei Zhang, Wei |
| author_facet | Feng, Tony Yun, Zhiwei Zhang, Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18557 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Arithmetic volumes of moduli stacks of Shtukas Feng, Tony Yun, Zhiwei Zhang, Wei Number Theory Algebraic Geometry 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. |
| title | Arithmetic volumes of moduli stacks of Shtukas |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2601.18557 |