Hirsch weight-filtered log crystalline complex and Hirsch weight-filtered log crystalline dga of a proper SNCL scheme in characteristic p>0

Fuente: arXiv
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Autor principal: Nakkajima, Yukiyoshi
Formato: Preprint
Publicado: 2020
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author Nakkajima, Yukiyoshi
author_facet Nakkajima, Yukiyoshi
contents We construct a theory of the derived PD-Hirsch extension of the log crystalline complex of a log smooth scheme and we construct a fundamental filtered dga $(H_{{\rm zar},{\rm TW}},P)$ and a fundamental filtered complex $(H_{\rm zar},P)$ for a simple normal crossing log scheme $X$ over a family of log points by using the log crystalline method in order to overcome obstacles arising from the incompatibility of the p-adic Steenbrink complexes in [M] and [Nak4] with the cup product of the log crystalline complex of $X$. When the base log scheme is the log point of a perfect field of characteristic $p>0$, we prove that $(H_{{\rm zar},{\rm TW}},P)$ and $(H_{\rm zar},P)$ is canonically isomorphic to Kim and Hain's filtered dga and their filtered complex in [KH], respectively.
format Preprint
id arxiv_https___arxiv_org_abs_2012_12981
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Hirsch weight-filtered log crystalline complex and Hirsch weight-filtered log crystalline dga of a proper SNCL scheme in characteristic p>0
Nakkajima, Yukiyoshi
Algebraic Geometry
We construct a theory of the derived PD-Hirsch extension of the log crystalline complex of a log smooth scheme and we construct a fundamental filtered dga $(H_{{\rm zar},{\rm TW}},P)$ and a fundamental filtered complex $(H_{\rm zar},P)$ for a simple normal crossing log scheme $X$ over a family of log points by using the log crystalline method in order to overcome obstacles arising from the incompatibility of the p-adic Steenbrink complexes in [M] and [Nak4] with the cup product of the log crystalline complex of $X$. When the base log scheme is the log point of a perfect field of characteristic $p>0$, we prove that $(H_{{\rm zar},{\rm TW}},P)$ and $(H_{\rm zar},P)$ is canonically isomorphic to Kim and Hain's filtered dga and their filtered complex in [KH], respectively.
title Hirsch weight-filtered log crystalline complex and Hirsch weight-filtered log crystalline dga of a proper SNCL scheme in characteristic p>0
topic Algebraic Geometry
url https://arxiv.org/abs/2012.12981