Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction. (15th October 2015) - DELBOURGO, DANIEL; LEI, ANTONIO
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 ∞ ≅ Z p ⋊ 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 M_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.