Comparison of relatively unipotent log de Rham fundamental groups. (English) Zbl 07726551
Memoirs of the American Mathematical Society 1430. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-6706-7/pbk; 978-1-4704-7572-7/ebook). v, 111 p. (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.
MSC:
| 14-02 | Research exposition (monographs, survey articles) pertaining to algebraic geometry |
| 14F35 | Homotopy theory and fundamental groups in algebraic geometry |
| 14F40 | de Rham cohomology and algebraic geometry |
| 14H10 | Families, moduli of curves (algebraic) |
| 14F30 | \(p\)-adic cohomology, crystalline cohomology |
| 14Gxx | Arithmetic problems in algebraic geometry; Diophantine geometry |
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