PreprintarXiv licencearXiv
On the variation of slopes over moduli stacks of Galois representations
Abstract
We determine how p-adic slopes of modular forms vary as their associated Galois representations modulo p vary over moduli of Galois representations. As a consequence, we show that the authors' ghost conjecture recently proven by Liu, Truong, Xiao, and Zhao is "stable under direct sums".
Related
- Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves
- Degenerations of shifted symplectic moduli stacks of sheaves
- Rationality of Kontsevich moduli of stable maps, and their Galois descents
- Locally analytic representations in mixed characteristic via stacks
- Lifting mod pn Galois representations
BibTeX
@misc{bergdall2026variation,
title = {{On the variation of slopes over moduli stacks of Galois representations}},
author = {John Bergdall and Robert Pollack},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12281},
eprint = {2609.12281},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12281},
}
RIS
TY - UNPB
TI - On the variation of slopes over moduli stacks of Galois representations
AU - John Bergdall
AU - Robert Pollack
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12281
UR - https://arxiv.org/abs/2609.12281
AB - We determine how p-adic slopes of modular forms vary as their associated Galois representations modulo p vary over moduli of Galois representations. As a consequence, we show that the authors' ghost conjecture recently proven by Liu, Truong, Xiao, and Zhao is "stable under direct sums".
ER -