PreprintCC BY-NC-ND 4.0arXiv
p-adic Hodge theory of unipotent completions revisited
Abstract
Let K/ℚp be a finite extension, and let X/K be an algebraic variety. We present a new proof that the unipotent completion of the étale fundamental group of XK̅ is a pro-de Rham representation, and show that it is pro-semi-stable whenever X has semi-stable étale cohomology. We also reprove, using syntomic methods, that it is pro-crystalline at integral base points whenever X admits a smooth proper formal model. All three proofs use the bar construction and are inspired by Wojtkowiak's approach to unipotent fundamental groups.
Related
- Maximal Unipotent Monodromy and p-adic Eigenvalue Formulas
- Harmonic Analysis on p-adic Unipotent Groups
- Uniform local models of quasi-unipotent p-adic differential equations
- An explicit form of the standard conjecture of Hodge type for Hermitian varieties, with p-adic applications
- Singular Hodge theory for combinatorial geometries
BibTeX
@misc{wild2026padic,
title = {{p-adic Hodge theory of unipotent completions revisited}},
author = {Ruth Wild},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17169},
eprint = {2610.17169},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17169},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - p-adic Hodge theory of unipotent completions revisited
AU - Ruth Wild
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17169
UR - https://arxiv.org/abs/2610.17169
AB - Let K/ℚ_p be a finite extension, and let X/K be an algebraic variety. We present a new proof that the unipotent completion of the étale fundamental group of X_K̅ is a pro-de Rham representation, and show that it is pro-semi-stable whenever X has semi-stable étale cohomology. We also reprove, using syntomic methods, that it is pro-crystalline at integral base points whenever X admits a smooth proper formal model. All three proofs use the bar construction and are inspired by Wojtkowiak's approach to unipotent fundamental groups.
ER -