Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction. (15th October 2015) - DELBOURGO, DANIEL; LEI, ANTONIO
Abstract: Let $E_{/{\mathbb{Q}}}$ be a semistable elliptic curve, and p ≠ 2 a prime of bad multiplicative reduction. For each Lie extension $\mathbb{Q}$ FT / $\mathbb{Q}$ with Galois group G ∞ ≅ $\mathbb{Z}$ p ⋊ $\mathbb{Z}$ 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 $\mathfrak{M}_{\mathcal{H}}$ ( 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.