# Twisting Commutative Algebraic Groups

 Title: Twisting Commutative Algebraic Groups Author: Mazur, Barry C.; Rubin, Karl; Silverberg, Alice Note: Order does not necessarily reflect citation order of authors. Citation: Mazur, Barry C., Karl Rubin, and Alice Silverberg. 2007. Twisting commutative algebraic groups. Journal of Algebra 314(1): 419-438. Full Text & Related Files: Mazur_TwistingCommutative.pdf (301.4Kb; PDF) Abstract: If $$V$$ is a commutative algebraic group over a field $$k$$, [View the MathML] source is a commutative ring that acts on $$V$$, and View the MathML source is a finitely generated free View the MathML source-module with a right action of the absolute Galois group of $$k$$, then there is a commutative algebraic group [View the MathML source] over $$k$$, which is a twist of a power of $$V$$. These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori over finite fields) and to the arithmetic of abelian varieties over number fields. For purposes of such applications we devote this article to making explicit this tensor product construction and its basic properties. Published Version: doi:10.1016/j.jalgebra.2007.02.052 Other Sources: http://arxiv.org/pdf/math/0609066v2 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10355841 Downloads of this work: