On Morphisms Between Connected Commutative Algebraic Groups over a Field of Characteristic 0

Difference algebraic subgroups of commutative algebraic groups over finite fields

We study the question of which torsion subgroups of commutative algebraic groups over finite fields are contained in modular difference algebraic groups for some choice of a field automorphism. We show that if G is a simple commutative algebraic group over a finite field of characteristic p, ` is a prime different from p, and for some difference closed field (K, σ) the `-primary torsion of G(K)...

Verifying Monoid and Group Morphisms over Strongly Connected Algebraic Automata

Automata theory has played an important role in theoretical computer science since last couple of decades. The algebraic automaton has emerged with several modern applications, for example, optimization of programs, design of model checkers, development of theorem provers because of having certain interesting properties and structures from algebraic theory of mathematics. Design of a complex sy...

THE abc THEOREM FOR COMMUTATIVE ALGEBRAIC GROUPS IN CHARACTERISTIC p

Buium proved what he called the abc theorem for abelian varieties over function fields in characteristic zero [3]. Using methods of algebraic model theory we prove an analog of his theorem for commutative algebraic groups in characteristic p. In what follows, k is an algebraically closed field of characteristic p, C is a smooth projective curve over k, and K = k(C) is the function field of C. I...

THE ab THEOREM FOR COMMUTATIVE ALGEBRAIC GROUPS IN CHARACTERISTIC p

Twisting Commutative Algebraic Groups

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...