论文标题
在de rham-witt综合体上方
On the de Rham-Witt complex over perfectoid rings
论文作者
论文摘要
修复一个奇怪的prime $ p $。本文的结果是在Hesselholt和Hesselholt-Madsen在$ p $ typical typical De Rham-Witt复合物中的工作中进行建模的。我们有两个主要结果。第一个是一个精确的序列，它描述了$ a $ a $ a $ a $ a $的限制图的内核，其中$ a $是代数扩展的整数环，$ \ mathbb {q} _p $，或$ a $ a $ as $ a $ as $ p $ p $ - tosorsion-torsion-torsion-torsion-torsion-torsion-torsion-torsion-torsion-torsion-torsion-tore-torsion-freepers-free Perfectoidoid ring。第二个结果是对$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ to $ p $ tose-tors-tors-tors-tors-forders perfectoid环的描述描述，其中包含$ p $ p $ poppower的统一根源。这两个结果都类似于Hesselholt和Madsen的结果。我们的主要贡献是将其结果扩展到某些完美环。我们还提供了这些结果的代数证明，而Hesselholt和Madsen的证明使用了拓扑。
Fix an odd prime $p$. The results in this paper are modeled after work of Hesselholt and Hesselholt-Madsen on the $p$-typical absolute de Rham-Witt complex in mixed characteristic. We have two primary results. The first is an exact sequence which describes the kernel of the restriction map on the de Rham-Witt complex over $A$, where $A$ is the ring of integers in an algebraic extension of $\mathbb{Q}_p$, or where $A$ is a $p$-torsion-free perfectoid ring. The second result is a description of the $p$-power torsion (and related objects) in the de Rham-Witt complex over $A$, where $A$ is a $p$-torsion-free perfectoid ring containing a compatible system of $p$-power roots of unity. Both of these results are analogous to results of Hesselholt and Madsen. Our main contribution is the extension of their results to certain perfectoid rings. We also provide algebraic proofs of these results, whereas the proofs of Hesselholt and Madsen used techniques from topology.
