2,359 research outputs found
Twisting commutative algebraic groups
If is a commutative algebraic group over a field , is a
commutative ring that acts on , and is a finitely generated free
-module with a right action of the absolute Galois group of , then there
is a commutative algebraic group over , which is a twist of
a power of . 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.Comment: To appear in Journal of Algebra. Minor changes from original versio
On the Picard group of a Delsarte surface
We suggest an algorithm computing, in some cases, an explicit generating set
for the N\'eron--Severi lattice of a Delsarte surface
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