Repository logo

Infoscience

  • English
  • French
Log In
Logo EPFL, École polytechnique fédérale de Lausanne

Infoscience

  • English
  • French
Log In
  1. Home
  2. Academic and Research Output
  3. Journal articles
  4. Unramified F-divided objects and the etale fundamental pro-groupoid in positive characteristic
 
Loading...
Thumbnail Image
research article

Unramified F-divided objects and the etale fundamental pro-groupoid in positive characteristic

Huang, Yuliang
•
Orecchia, Giulio  
•
Romagny, Matthieu
January 1, 2022
Geometry & Topology

Let X /S be a flat algebraic stack of finite presentation. We define a new & eacute;tale fundamental pro-groupoid pi(1)(X /S), generalizing Grothendieck's enlarged & eacute;tale fundamental group from SGA 3 to the relative situation. When S is of equal positive characteristic p, we prove that pi(1)(X /S) naturally arises as colimit of the system of relative Frobenius morphisms X -> X-p/S -> X-p2/S -> center dot center dot center dot in the pro-category of Deligne Mumford stacks. We give an interpretation of this result as an adjunction between pi(1) and the stack Fdiv of F -divided objects. In order to obtain these results, we study the existence and properties of relative perfection for algebras in characteristic p.

  • Details
  • Metrics
Type
research article
DOI
10.2140/gt.2022.26.3221
Web of Science ID

WOS:000946189900007

Author(s)
Huang, Yuliang
•
Orecchia, Giulio  
•
Romagny, Matthieu
Date Issued

2022-01-01

Publisher

GEOMETRY & TOPOLOGY PUBLICATIONS

Published in
Geometry & Topology
Volume

26

Issue

7

Start page

3221

End page

3306

Subjects

Mathematics

•

modules

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
ARG  
Available on Infoscience
April 10, 2023
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/196826
Logo EPFL, École polytechnique fédérale de Lausanne
  • Contact
  • infoscience@epfl.ch

  • Follow us on Facebook
  • Follow us on Instagram
  • Follow us on LinkedIn
  • Follow us on X
  • Follow us on Youtube
AccessibilityLegal noticePrivacy policyCookie settingsEnd User AgreementGet helpFeedback

Infoscience is a service managed and provided by the Library and IT Services of EPFL. © EPFL, tous droits réservés