Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

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
Full-text PDF

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 [Enhancements On Off] (What's this?)


Additional Information

Richard Hain
Affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708-0320
Email: hain@math.duke.edu

DOI: https://doi.org/10.1090/S1056-3911-2013-00598-6
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.

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website