Canonical representatives and interval independence in Ekedahl's equivalence

Source abstract

Ekedahl's equivalence reconstructs coherent Raynaud complexes from coherent F-gauges by a completed derived functor. We study this inverse before totalization. At a fixed finite level, we construct finite projective resolutions and express the inverse as a tensor product with a complex of bimodules. Its cohomology in the resolution direction gives actual R-complex representatives of diagonal cohomology. We prove that these representatives are independent of the interval and obtain an exact fully faithful functor from the diagonal heart to Ch(R), splitting localization. Finally, we compute the domino factors for three cyclic crystalline presentations of supergeneral abelian threefolds. The resulting elementary factor types are {2,3,4}, {2,3,7}, and {2,3,6}.