Accepted version, 420.1Kb
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
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.
Cambridge University Press (CUP)
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.