AI 中文总结
本文研究Ekedahl等价中逆过程的有限层级构造，证明其典范代表与区间无关，并给出超一般阿贝尔三维簇的domino因子类型。
AI 中文摘要
Ekedahl等价通过一个完备的导出函子，从相干F-规范重构相干Raynaud复形。我们在全总化之前研究这一逆过程。在固定的有限层级，我们构造有限射影分解，并将逆过程表示为与一个双模复形的张量积。其在分解方向上的上同调给出了对角上同调的实际R-复形代表。我们证明这些代表与区间无关，并得到一个从对角心到Ch(R)的精确全忠实函子，分裂局部化。最后，我们计算超一般阿贝尔三维簇的三个循环晶体表示的domino因子。所得的基本因子类型为{2,3,4}、{2,3,7}和{2,3,6}。
英文摘要
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}.
Comments22 pages
