Publications [#287265] of Richard Hain

Papers Published

1. Hain, R, Remarks on non-abelian cohomology of proalgebraic groups, Journal of Algebraic Geometry, vol. 22 no. 3 (June, 2013), pp. 581-598, American Mathematical Society (AMS), ISSN 1056-3911 [arXiv:1009.3662], [S1056-3911-2013-00598-6], [doi]
   (last updated on 2026/01/15)

   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 ¹nab(G,P) is a scheme. The argument G is a proalgebraic group; the coefficient group P is prounipotent with trivial center and endowed with an outer action of G. This outer action uniquely determines an extension Ĝ of G by P. With suitable hypotheses, the scheme H¹ nab(G,P) parametrizes the P conjugacy classes of sections of Ĝ →G. © 2013 University Press, Inc.