论文标题
绝对整体封闭的Cohen-Macaulayness
Cohen-Macaulayness of absolute integral closures
论文作者
论文摘要
我们证明，Modulo Prime $ p $的任何功能，出色的Noetherian域的绝对整体关闭是Cohen-Macaulay。还建立了一个分级模拟，产生了Kodaira的变体消失在混合特征中的“到有限盖”。我们的主要工具是（log）Prismatic共同体（在混合特征中产生Frobenius动作）和$ p $ -Adic Riemann-Hilbert functor，用于可构造的étale$ \ Mathbf {f} _p $ -sheaves在$ p $ addic Field上（几乎可以控制的完美的Proistic Proist prismology coalology of Collectife）。
We prove that, modulo any power of a prime $p$, the absolute integral closure of an excellent noetherian domain is Cohen-Macaulay. A graded analog is also established, yielding variants of Kodaira vanishing "up to finite covers" in mixed characteristic. Our main tools are (log) prismatic cohomology (which yields a Frobenius action in mixed characteristic) and the $p$-adic Riemann-Hilbert functor for constructible étale $\mathbf{F}_p$-sheaves on varieties over a $p$-adic field (which almost controls perfectified prismatic cohomology).
