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arXiv · 2609.39293

Ekedahl's Equivalence Explained

Yuan Yang
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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.

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Yuan Yang. 2026-10-09. Ekedahl's Equivalence Explained. https://arxiv.org/abs/2609.39293

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