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Stanley-Reisner Theory in Mixed Characteristic
Abstract
We discuss a class of mixed characteristic rings defined analogously to Stanley-Reisner rings by replacing one variable with a uniformizing parameter for a discrete valuation ring. We adapt Hochster's formula for Tor and Ext modules, Hochster's formula for local cohomology, and Terai's criterion for Serre conditions to this new setting; one of the tools needed is cellular sheaf cohomology, for which we give a brief treatment.
Related
- Cube-freeness and a square formula for canonical trace ideals of Stanley--Reisner rings
- Characterization of Stanley-Reisner varieties by their automorphism group
- The Negami Polynomial and Broken-Circuit Stanley--Reisner Rings
- Powers of Alexander Duals of Stanley-Reisner Ideals of Chessboard Complexes
- Homology of non-matching complexes under edge additions and applications to their Stanley-Reisner ideals
BibTeX
@misc{hochster2026stanleyreisner,
title = {{Stanley-Reisner Theory in Mixed Characteristic}},
author = {Mel Hochster and Olivia Strahan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38947},
eprint = {2609.38947},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38947},
}
RIS
TY - UNPB
TI - Stanley-Reisner Theory in Mixed Characteristic
AU - Mel Hochster
AU - Olivia Strahan
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.38947
UR - https://arxiv.org/abs/2609.38947
AB - We discuss a class of mixed characteristic rings defined analogously to Stanley-Reisner rings by replacing one variable with a uniformizing parameter for a discrete valuation ring. We adapt Hochster's formula for Tor and Ext modules, Hochster's formula for local cohomology, and Terai's criterion for Serre conditions to this new setting; one of the tools needed is cellular sheaf cohomology, for which we give a brief treatment.
ER -