Computations in non-commutative Iwasawa theory

Abstract

We study special values of L-functions of elliptic curves over Q twisted by Artin representations that factor through a false Tate curve extension $Q({\mu }_p^{\infty },\sqrt[p^{\infty }]{m})/Q$. In this setting, we explain how to compute L-functions and the corresponding Iwasawa-theoretic invariants of non-abelian twists of elliptic curves. Our results provide both theoretical and computational evidence for the main conjecture of non-commutative Iwasawa theory.

60 pages; with appendix by John Coates and Ramdorai Sujatha

References in corpus (1)

• Algebraicity of L-values for elliptic curves in a false Tate curve tower

Cited by in corpus (12)

• On the Birch-Swinnerton-Dyer quotients modulo squares
• On the growth of Mordell-Weil ranks in $p$-adic Lie extensions
• A remark on the ${\mathfrak{M}}_H(G)$-conjecture and Akashi series
• Growth of Sha in towers for isogenous curves
• Algebraic functional equations and completely faithful Selmer groups
• Selmer groups of elliptic curves in degree $p$ extensions
• Control theorem and functional equation of Selmer groups over $p$-adic Lie extensions
• Non-commutative p-adic L-functions for supersingular primes
• Structure of fine Selmer groups over ${\mathbb{Z}}_p$-extensions
• Akashi series, characteristic elements and congruence of Galois representations
• Congruences for Convolutions of Hilbert Modular Forms
• On order of vanishing of characteristic elements