ON THE BUMPY FUNDAMENTAL GROUP SCHEME

Abstract : In this short paper we first recall the definition and the construction of the fundamental group scheme of a scheme X in the known cases: when it is defined over a field and when it is defined over a Dedekind scheme. It classifies all the finite (or quasi-finite) fpqc torsors over X. When X is defined over a noetherian regular scheme S of any dimension we do not know if such an object can be constructed. This is why we introduce a new category, containing the fpqc torsors, whose objects are torsors for a new topology. We prove that this new category is cofiltered thus generating a fundamental group scheme over S, said bumpy as it may not be flat in general. We prove that it is flat when S is a Dedekind scheme, thus coinciding with the classical one.
Document type :
Directions of work or proceedings
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.univ-cotedazur.fr/hal-01342090
Contributor : Marco Antei <>
Submitted on : Tuesday, July 5, 2016 - 2:00:09 PM
Last modification on : Thursday, May 3, 2018 - 1:32:58 PM
Long-term archiving on : Thursday, October 6, 2016 - 11:45:47 AM

File

1511.07331v1.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01342090, version 1

Collections

Citation

Marco Antei. ON THE BUMPY FUNDAMENTAL GROUP SCHEME. France. 2015. ⟨hal-01342090⟩

Share

Metrics

Record views

100

Files downloads

306