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Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.

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Grothendieck-Messing theory

Hello, I would like to work out some examples of deformation of isogenies via Grothendieck-Messing theory. Let's take an easy example: Let A be an abelian variety over $k=\overline{\mathbb{F}_p}$ and …