@article{cf09b44822a94abc92162442a8fc7c42,
title = "The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme",
abstract = "We define the algebraic fundamental group π 1(G) of a reductive group scheme G over an arbitrary non-empty base scheme and show that the resulting functor G{mapping} π1(G) is exact.",
keywords = "Algebraic fundamental group, Reductive group scheme",
author = "Mikhail Borovoi and Gonz{\'a}lez-Avil{\'e}s, {Cristian D.}",
note = "Funding Information: Mikhail Borovoi was partially supported by the Hermann Minkowski Center for Geometry. Cristian D. Gonz{\'a}lez-Avil{\'e}s was partially supported by Fondecyt grant 1120003. The authors are very grateful to Brian Conrad for proving [5, Proposition B.3.8], which we used in the proof of Proposition 2.2 and in a construction in Remark 2.12. We are grateful to Joseph Bernstein for his help in proving Lemma 2.6, and to Jean-Louis Colliot-Th{\'e}l{\`e}ne for most helpful discussions. We thank the anonymous referees for their helpful remarks. This paper was completed during a stay of both authors at the Max-Planck-Institut f{\"u}r Mathematik, Bonn, and we are very grateful to this institute for hospitality, support and excellent working conditions.",
year = "2014",
month = jan,
doi = "10.2478/s11533-013-0363-0",
language = "אנגלית",
volume = "12",
pages = "545--558",
journal = "Open Mathematics",
issn = "1895-1074",
publisher = "Walter de Gruyter GmbH",
number = "4",
}