## Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction

##### Files

Accepted version, 420.1Kb

##### Citation

Delbourgo, D., & Lei, A. (2015). Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction. Mathematical Proceedings of the Cambridge Philosophical Society. http://doi.org/10.1017/S0305004115000535

Permanent Research Commons link: http://hdl.handle.net/10289/10022

##### Abstract

Let E/ℚ be a semistable elliptic curve, and p ≠ 2 a prime of bad multiplicative reduction. For each Lie extension ℚ FT / ℚ with Galois group G∞ ≅ℤр ⋊ ℤ p ×, we construct p-adic L-functions interpolating Artin twists of the Hasse–Weil L-series of the curve E. Through the use of congruences, we next prove a formula for the analytic λ-invariant over the false Tate tower, analogous to Chern–Yang Lee's results on its algebraic counterpart. If one assumes the Pontryagin dual of the Selmer group belongs to the ℳℌ(G∞)-category, the leading terms of its associated Akashi series can then be computed, allowing us to formulate a non-commutative Iwasawa Main Conjecture in the multiplicative setting.

##### Date

2015##### Type

##### Publisher

Cambridge University Press (CUP)

##### Rights

This is an author’s accepted version of an article published in the journal: Mathematical Proceedings of the Cambridge Philosophical Society. Copyright © Cambridge Philosophical Society 2015.