Remarks on non-abelian cohomology of proalgebraic groups
Author:
Richard Hain
Journal:
J. Algebraic Geom. 22 (2013), 581-598
DOI:
https://doi.org/10.1090/S1056-3911-2013-00598-6
Published electronically:
March 21, 2013
MathSciNet review:
3048547
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Abstract |
References |
Additional Information
Abstract: In this paper we develop a theory of non-abelian cohomology for proalgebraic groups which is used in J. Amer. Math. Soc. 24 (2011), 709–769 to study the unipotent section conjecture. The non-abelian cohomology $H^1_{\mathrm {nab}}(\mathcal {G},\mathcal {P})$ is a scheme. The argument $\mathcal {G}$ is a proalgebraic group; the coefficient group $\mathcal {P}$ is prounipotent with trivial center and endowed with an outer action of $\mathcal {G}$. This outer action uniquely determines an extension $\widehat {\mathcal {G}}$ of $\mathcal {G}$ by $\mathcal {P}$. With suitable hypotheses, the scheme $H^1_{\mathrm {nab}} (\mathcal {G},\mathcal {P})$ parametrizes the $\mathcal {P}$ conjugacy classes of sections of $\widehat {\mathcal {G}} \to \mathcal {G}$.
References
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References
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Additional Information
Richard Hain
Affiliation:
Department of Mathematics, Duke University, Durham, North Carolina 27708-0320
MR Author ID:
79695
ORCID:
0000-0002-7009-6971
Email:
hain@math.duke.edu
Received by editor(s):
October 13, 2010
Received by editor(s) in revised form:
April 11, 2011
Published electronically:
March 21, 2013
Additional Notes:
Supported in part by National Science Foundation grant DMS-1005675.
Article copyright:
© Copyright 2013
University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.