Twisting Commutative Algebraic Groups

By Barry Mazur, Karl Rubin, Alice Silverberg. 2006

67 citations recorded by the source corpus.

Abstract If V is a commutative algebraic group over a field k , O is a commutative ring that acts on V , and I is a finitely generated free O -module with a right action of the absolute Galois group of k , then there is a commutative algebraic group I ⊗ O V 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e20bbf7af2f4f30dc5b3b46112685c8bb167261

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In Geometry and Topology

1. Barry Mazur
2. Karl Rubin
3. Tim Dokchitser
4. Vladimir Dokchitser
5. Antonio Lei
6. Florian Sprung
7. Jorma Jormakka

In Mathematical Physics

1. Barry Mazur
2. Karl Rubin
3. Antonio Lei
4. Florian Sprung

Citations in the corpus

• Finding Large Selmer Rank via an Arithmetic Theory of Local Constants (2005, methodology): “as in Definition 1.1 (and §6) of [ MRS ].”