Comparison of Relatively Unipotent Log de Rham Fundamental Groups / Bruno Chiarellotto, Valentina Di Proietto, and Atsushi Shiho.

Format:

• Book

Author/Creator:

• Chiarellotto, Bruno, 1961- author.
• Di Proietto, Valentina, author.
• Shiho, Atsushi, author.

Series:

• Memoirs of the American Mathematical Society ; Volume 288.
• Memoirs of the American Mathematical Society Series ; Volume 288

Language:

English

Subjects (All):

• Fundamental groups (Mathematics).
• Homology theory.

Physical Description:

1 online resource (124 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"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"-- Provided by publisher.

Contents:

• Cover
• Title page
• Introduction
• Conventions
• Acknowledgements
• Chapter 1. Preliminaries
• Chapter 2. Relative Tannakian theory
• Chapter 3. Construction of Hadian, Andreatta-Iovita-Kim and Lazda
• Chapter 4. Relative minimal model of Navarro Aznar
• Chapter 5. Relative bar construction
• Chapter 6. Calculation of monodromy for stable log curves
• 6.1. Statement of main result and first reductions
• 6.2. Calculation of Lie algebra
• 6.3. Tangential sections
• 6.4. Calculation of monodromy (I)
• 6.5. Calculation of monodromy (II)
• 6.6. Calculation of monodromy (III)
• 6.7. End of the proof
• 6.8. Application to Andreatta-Iovita-Kim theorem
• Bibliography
• Back Cover.

Notes:

• Description based on print version record.
• Includes bibliographical references.

Other Format:

Print version: Chiarellotto, Bruno Comparison of Relatively Unipotent Log de Rham Fundamental Groups

ISBN:

• 9781470475727
• 1470475723