PreprintCC BY 4.0arXiv
Ekedahl's Equivalence Explained
Abstract
Ekedahl's theory relates diagonal complexes to F-gauges, but turning this equivalence into explicit calculations requires careful control of its constructions. These notes explain the equivalence and clarify the generators-and-relations definition of rmt. At each finite level, we construct bounded projective resolutions of bounded coherent gauge complexes by finite sums of the standard generators. Morita equivalence expresses rmt as a tensor product functor. Comparing the constructions across levels yields an exact fully faithful embedding of the diagonal heart into Ch(R). Finally, we compute three distinct domino types arising from abelian threefolds that are all supergeneral.
Related
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- Ekedahl-Oort strata meeting the supersingular locus
- Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties
- The Complexity of Conjugacy, Orbit Equivalence, and von Neumann Equivalence of Actions of Nonamenable Groups
- Thurston equivalence of topological polynomials
BibTeX
@misc{yang2026ekedahls,
title = {{Ekedahl's Equivalence Explained}},
author = {Yuan Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39293},
eprint = {2609.39293},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39293},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ekedahl's Equivalence Explained
AU - Yuan Yang
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.39293
UR - https://arxiv.org/abs/2609.39293
AB - Ekedahl's theory relates diagonal complexes to F-gauges, but turning this equivalence into explicit calculations requires careful control of its constructions. These notes explain the equivalence and clarify the generators-and-relations definition of rmt. At each finite level, we construct bounded projective resolutions of bounded coherent gauge complexes by finite sums of the standard generators. Morita equivalence expresses rmt as a tensor product functor. Comparing the constructions across levels yields an exact fully faithful embedding of the diagonal heart into Ch(R). Finally, we compute three distinct domino types arising from abelian threefolds that are all supergeneral.
ER -