Franco-Asian Summer School on Arithmetic Geometry

Collection Franco-Asian Summer School on Arithmetic Geometry

Organizer(s) Ahmed Abbes (CNRS & IHÉS), Ana Caraiani (Imperial College London ), Ariane Mézard (Sorbonne Université), Takeshi Saito (University of Tokyo), Takeshi Tsuji (The University of Tokyo), Daxin Xu (Chinese Academy of Sciences), Weizhe Zheng (Chinese Academy of Sciences).

Date(s) 30/05/2022 - 03/06/2022

linked URL https://www.ihes.fr/~abbes/Luminy/luminy2022.html

00:00:00 / 00:00:00

17 23

Graded logarithmic geometry and valuative spaces

By Quentin Guignard

We introduce a generalization of Temkin's reduction in an absolute setting. It takes the form of a category of graded log schemes, containing valuative spaces as a full subcategory, as well as more exotic objects such as the reduction mod p^n of a p-adic rigid space. We will compare the log étale and log syntomic topologies on these objects, and we will show that the ramification filtrations of Abbes-Saito, Saito and Kato-Thatte measure precisely the lack of topological invariance of the corresponding log syntomic toposes. As a byproduct, we recover and generalize results of Deligne and Hattori on the ramification of extensions of truncated discrete valuation rings.

Information about the video

Date of recording 31/05/2022
Date of publication 20/06/2022
Institution IHES
Language English
Audience Researchers, Graduate Students
Format MP4
Venue CIRM

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