AI 中文总结
本文研究几何不可约反常层在算术基上的延拓，证明算术柏原猜想并推广分解定理与硬Lefschetz定理。
AI 中文摘要
我们将几何不可约的反常层展开。在算术基概形上，此类层从一般纤维延拓为基概形稠密开集上的相对反常且普遍局部非循环的层。作为应用，我们证明了Esnault和Kerz关于等特征几何特征的算术柏原猜想，并将算术复形的分解定理推广到可分闭域上有限生成的域。我们还恢复了算术反常层的硬Lefschetz定理。
英文摘要
We spread out geometrically irreducible perverse sheaves. Over an arithmetic base scheme, such sheaves extend from the generic fiber to a relatively perverse, universally locally acyclic sheaf over a dense open of the base scheme. As an application, we prove the arithmetic Kashiwara conjecture by Esnault and Kerz for geometric traits in equicharacteristic and generalize the decomposition theorem for arithmetic complexes to fields finitely generated over a separably closed field. We also recover the Hard Lefschetz theorem for arithmetic perverse sheaves.
