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Crystals and the parabolicity conjecture
Abstract
These notes introduce crystals and crystalline Dieudonné theory through the example of abelian varieties. After discussing p-divisible groups, F-isocrystals, slope filtrations, and overconvergence, we explain the parabolicity theorem for F-isocrystals and some of its applications to monodromy and Hecke orbits. Two appendices formulate research projects on isocrystals over formal schemes and on monodromy beyond the constant-slope setting. The exposition is intended for readers familiar with basic algebraic geometry and the étale and fppf topologies; prior knowledge of Witt vectors is helpful but not required.
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BibTeX
@misc{daddezio2026crystals,
title = {{Crystals and the parabolicity conjecture}},
author = {Marco D'Addezio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15521},
eprint = {2610.15521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15521},
}
RIS
TY - UNPB
TI - Crystals and the parabolicity conjecture
AU - Marco D'Addezio
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15521
UR - https://arxiv.org/abs/2610.15521
AB - These notes introduce crystals and crystalline Dieudonné theory through the example of abelian varieties. After discussing p-divisible groups, F-isocrystals, slope filtrations, and overconvergence, we explain the parabolicity theorem for F-isocrystals and some of its applications to monodromy and Hecke orbits. Two appendices formulate research projects on isocrystals over formal schemes and on monodromy beyond the constant-slope setting. The exposition is intended for readers familiar with basic algebraic geometry and the étale and fppf topologies; prior knowledge of Witt vectors is helpful but not required.
ER -