Projective Decomposition and Intersection Cohomology of Rigid Spaces
Abstract
We prove a rigid analytic analogue of the Beilinson--Bernstein--Deligne decomposition theorem for projective morphisms over p-adic fields, with Qℓ-coefficients for every prime ℓ, including ℓ=p. As an application, we show that the p-adic intersection cohomology of every proper rigid analytic space is de Rham. We also establish an independent criterion for de Rham intersection cohomology with local coefficients in terms of the dimension of the boundary, yielding further results for curves, surfaces, and finite covers. For finite coefficients of characteristic different from p, we obtain isotropic analytic upper bounds for singular support and prove that singular support is analytic and Lagrangian for complexes supported in dimension at most one.
Related
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- ℓ-Independence, slopes, and weights of ℓ-adic cohomology groups of rigid spaces
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- Effective Results for Foliations on Smooth Projective Complete Intersection Surfaces
BibTeX
@misc{yang2026projective,
title = {{Projective Decomposition and Intersection Cohomology of Rigid Spaces}},
author = {Jiawei Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25321},
eprint = {2610.25321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25321},
note = {CC0},
}
RIS
TY - UNPB
TI - Projective Decomposition and Intersection Cohomology of Rigid Spaces
AU - Jiawei Yang
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25321
UR - https://arxiv.org/abs/2610.25321
AB - We prove a rigid analytic analogue of the Beilinson--Bernstein--Deligne decomposition theorem for projective morphisms over p-adic fields, with Q_ℓ-coefficients for every prime ℓ, including ℓ=p. As an application, we show that the p-adic intersection cohomology of every proper rigid analytic space is de Rham. We also establish an independent criterion for de Rham intersection cohomology with local coefficients in terms of the dimension of the boundary, yielding further results for curves, surfaces, and finite covers. For finite coefficients of characteristic different from p, we obtain isotropic analytic upper bounds for singular support and prove that singular support is analytic and Lagrangian for complexes supported in dimension at most one.
ER -