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Comparison of Relatively Unipotent Log de Rham Fundamental Groups
About this Title
Bruno Chiarellotto, Valentina Di Proietto and Atsushi Shiho
Publication: Memoirs of the American Mathematical Society
Publication Year:
2023; Volume 288, Number 1430
ISBNs: 978-1-4704-6706-7 (print); 978-1-4704-7572-7 (online)
DOI: https://doi.org/10.1090/memo/1430
Published electronically: August 7, 2023
Table of Contents
Chapters
- Introduction
- 1. Preliminaries
- 2. Relative Tannakian theory
- 3. Construction of Hadian, Andreatta–Iovita–Kim and Lazda
- 4. Relative minimal model of Navarro Aznar
- 5. Relative bar construction
- 6. Calculation of monodromy for stable log curves
Abstract
In this paper, we prove compatibilities of various definitions of relatively unipotent log de Rham fundamental groups for certain proper log smooth integral morphisms of fine log schemes of characteristic zero. Our proofs are purely algebraic. As an application, we give a purely algebraic calculation of the monodromy action on the unipotent log de Rham fundamental group of a stable log curve. As a corollary we give a purely algebraic proof to the transcendental part of Andreatta–Iovita–Kim’s article: obtaining in this way a complete algebraic criterion for good reduction for curves.- Ahmed Abbes, Michel Gros, and Takeshi Tsuji, The $p$-adic Simpson correspondence, Annals of Mathematics Studies, vol. 193, Princeton University Press, Princeton, NJ, 2016. MR 3444777, DOI 10.1515/9781400881239
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