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Month: August 2015

Kummer theory and the weak Mordell-Weil theorem

In this post we discuss the notion of Kummer theory in its general form, and how this leads to a proof of the (weak) Mordell-Weil theorem.

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Posted in Algebraic Geometry, Etale Cohomology, Number Theory and tagged abelian varieties, arithmetic geometry, etale cohomology, kummer theory, mordell-weil theorem, mordell-weil theorem proof, principal homogenous space, proof, torsor, Weak Mordell-Weil theorem on August 17, 2015 by alexyoucis. 4 Comments

p-divisible groups, formal groups, and the Serre-Tate theorem

In this post we discuss the basic theory of p-divisible groups, their relationship to formal groups, and the Serre-Tate theorem.

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Posted in Algebraic Geometry, Algebraic Groups, Galois Representations, Number Theory and tagged abelian varieties, Algebraic Geometry, algebraic groups, arithmetic geometry, crystalline cohomology, finite flat group schemes, formal groups, Formal schemes, Formal schemes intuition, number theory, p-adic Hodge theory, p-divisible groups, Serre-Tate theorem on August 10, 2015 by alexyoucis. 3 Comments

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