Modular Curves and Abelian Varieties [Paperback]

Stable reduction of modular curves.- On p-adic families of automorphic forms.- ?-curves and abelian varieties of GL2-type from dihedral genus 2 curves.- The old subvariety of J0(NM).- Irreducibility of Galois actions on level 1 Siegel cusp forms.- On elliptic K-curves.- ?-curves and Galois representations.- On the local behaviour of ordinary modular Galois representations.- Arithmetic of ?-curves.- Serres conjecture for mod 7 Galois representations.- Pairings in the arithmetic of elliptic curves.- Explicit parametrizations of ordinary and supersingular regions of X0(Pn).- Elliptic ?-curves with complex multiplication.- Abelian varieties over ? with large endomorphism algebras and their simple components over ?.- Abelian varieties over ? and modular forms.- Shimura curves embedded in Igusas threefold.- Shafarevich-Tate groups of nonsquare order.

Includes recent contributions on modular curves and their Jacobians as well as such seminal works as Kenneth Ribet's article Abelian varieties over the rationals and modular forms , Elisabeth Pyle's 1995 dissertation on abelian varieties over the rationals with large endomorphism algebras, and Noam Elkies' 1993 manuscript on elliptic k-curves

Springer Book Archives