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Restrictions on the prime-to-$p$ fundamental group of a smooth projective variety

Part of: Curves

Published online by Cambridge University Press:  06 March 2015

Donu Arapura
Donu Arapura*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA email [email protected]
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Abstract

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The goal of this paper is to obtain restrictions on the prime-to-$p$ quotient of the étale fundamental group of a smooth projective variety in characteristic $p\geqslant 0$. The results are analogues of some theorems from the study of Kähler groups. Our first main result is that such groups are indecomposable under coproduct. The second result gives a classification of the pro-$\ell$ parts of one-relator groups in this class.

Keywords

fundamental groupprojective variety

MSC classification

Primary: 14H30: Coverings, fundamental group
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 6 , June 2015 , pp. 1083 - 1095
Copyright
© The Author 2015 

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