Harder-Narasimhan filtration of torsion F-gauges
Abstract
We establish a Harder-Narasimhan theory for torsion coherent F-gauges over a perfect field k of positive characteristic and completely classify its stable objects. Our construction uses Ekedahl's derived equivalence with coherent complexes over the Raynaud ring, where the theory refines his half-integral type filtration on diagonal dominoes. At each finite rational slope d/q in lowest terms, there is a unique stable diagonal domino up to Breuil-Kisin twist, constructed explicitly from the corresponding Christoffel word. The semistable category of this slope is equivalent to a product of q copies of the zero-slope category. The classification of stable objects corrects Ekedahl's classification of weakly simple diagonal dominoes of type 1/2. The theory upgrades to a locally finite Bridgeland stability condition on Perftor(kSyn).
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BibTeX
@misc{zhang2026hardernarasimhan,
title = {{Harder-Narasimhan filtration of torsion F-gauges}},
author = {Yuanning Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27089},
eprint = {2609.27089},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27089},
}
RIS
TY - UNPB
TI - Harder-Narasimhan filtration of torsion F-gauges
AU - Yuanning Zhang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27089
UR - https://arxiv.org/abs/2609.27089
AB - We establish a Harder-Narasimhan theory for torsion coherent F-gauges over a perfect field k of positive characteristic and completely classify its stable objects. Our construction uses Ekedahl's derived equivalence with coherent complexes over the Raynaud ring, where the theory refines his half-integral type filtration on diagonal dominoes. At each finite rational slope d/q in lowest terms, there is a unique stable diagonal domino up to Breuil-Kisin twist, constructed explicitly from the corresponding Christoffel word. The semistable category of this slope is equivalent to a product of q copies of the zero-slope category. The classification of stable objects corrects Ekedahl's classification of weakly simple diagonal dominoes of type 1/2. The theory upgrades to a locally finite Bridgeland stability condition on Perf_tor(k^Syn).
ER -