SFU Number Theory and Algebraic Geometry Seminar: Pijush Pratim Sarmah

Every curve has an abelian variety associated to it, called the Jacobian. Poincaré's total reducibility theorem states that any abelian variety is isogenuous to a product of simple abelian varieties. We are interested to know this decomposition for Jacobians of smooth curves in abelian surfaces. Using Kani and Rosen's strikingly simple yet powerful theorem that relates subgroups of automorphism groups with isogeny relations on Jacobians, we will decompose Jacobians of certain curves coming from linear systems of polarizations on abelian surfaces and comment on curve coverings.