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Books Year : 2015

ON THE BUMPY FUNDAMENTAL GROUP SCHEME

Marco Antei
  • Function : Scientific advisor

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.
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Dates and versions

hal-01342090 , version 1 (05-07-2016)

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  • HAL Id : hal-01342090 , version 1

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Marco Antei (Dir.). ON THE BUMPY FUNDAMENTAL GROUP SCHEME. 2015. ⟨hal-01342090⟩
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