某些Azumaya代数在正特征环面和超环面簇上的Étale分裂
Étale Splittings of Certain Azumaya Algebras on Toric and Hypertoric Varieties in Positive Characteristic
摘要：
对正特征域上的光滑复曲面簇X，构造了一个T-等变代数覆盖Y \rightarrow T^*X^{（1）}，使X上的结晶微分算子层平凡化.这种平凡化是用来表明，层的微分算子是一个平凡的Azumaya代数沿纤维的矩映射。然后将这一结果推广到某些超环面簇上的Azumaya代数，其整体瓣是超环面包络代数的正特征中心约化。一个标准的派生Beilinson-Bernstein局部化定理，然后制定。
英文摘要：
For a smooth toric variety X over a field of positive characteristic, a T-equivariant étale cover Y \rightarrow T^*X^{(1)} trivializing the sheaf of crystalline differential operators on X is constructed. This trivialization is used to show that the sheaf of differential operators is a trivial Azumaya algebra along the fibers of the moment map. This result is then extended to certain Azumaya algebras on hypertoric varieties, whose global sections are central reductions of the hypertoric enveloping algebra in positive characteristic. A criteria for a derived Beilinson-Bernstein localization theorem is then formulated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
