Franco-Asian Summer School on Arithmetic Geometry in Luminy / Ecole d'été franco-asiatique sur la géométrie arithmétique à Luminy

Collection Franco-Asian Summer School on Arithmetic Geometry in Luminy / Ecole d'été franco-asiatique sur la géométrie arithmétique à Luminy

Organizer(s) Abbes, Ahmed ; Mézard, Ariane ; Saito, Takeshi ; Zheng, Weizhe
Date(s) 30/05/2022 - 03/06/2022
linked URL https://conferences.cirm-math.fr/2534.html
00:00:00 / 00:00:00
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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.

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Citation data

  • DOI 10.24350/CIRM.V.19927603
  • Cite this video Guignard, Quentin (31/05/2022). Graded logarithmic geometry and valuative spaces. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19927603
  • URL https://dx.doi.org/10.24350/CIRM.V.19927603

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