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SUMMARY:The étale and pro-étale exodromy theorems [MPIM]
DTSTART:20251202T134500Z
DTEND:20251202T150000Z
DTSTAMP:20260420T154300Z
UID:indico-event-958@math-events.uni-bonn.de
DESCRIPTION:Speakers: Remy van Dobben de Bruyn (MPIM)\n\nMinicourse on the
  étale and pro-étale exodromy theorems\nÉtale sheaves on the spectrum o
 f a field can be understood as sets with a continuous action of the Galois
  group. A similar classification is available for locally constant sheaves
  on an arbitrary base scheme. In 2018\, Barwick–Glasman–Haine proved a
  far reaching generalisation of this result\, classifying constructible é
 tale sheaves on a scheme as continuous representations of a profinite cate
 gory they call the Galois category. This was then extended to pro-étale s
 heaves by Sebastian Wolf in 2022.\nIn this minicourse\, I will explain a n
 ew and more geometric proof of the étale and pro-étale exodromy theorems
 \, obtained in upcoming joint work with Sebastian Wolf. The key player in 
 our method is the condensed category of points of the étale topos. We giv
 e an explicit computation of this condensed category in terms of the w-str
 ictly local schemes constructed in Bhatt–Scholze's work on the pro-étal
 e topology. This generalises the computation of the classical (non-condens
 ed) category of points in SGA 4 in terms of strictly Henselian rings. The 
 pro-étale exodromy theorem follows quickly from our computation\, and the
  étale version is deduced from the pro-étale one.\nPrerequisites: beside
 s a basic knowledge of algebraic geometry and category theory\, we will as
 sume familiarity with the étale and pro-étale topology on a scheme\, and
  the basics of the theory of condensed sets (we do not need much beyond th
 e first definitions). We will not assume any knowledge of higher category 
 theory\, but we will indicate where ∞-categorical statements can be obta
 ined.\n\nhttps://math-events.uni-bonn.de/event/958/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/958/
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