CODIMENSION TWO CYCLES IN IWASAWA THEORY AND ELLIPTIC CURVES WITH SUPERSINGULAR REDUCTION. (2019) - LEI, ANTONIO; PALVANNAN, BHARATHWAJ
Abstract : A result of Bleher, Chinburg, Greenberg, Kakde, Pappas, Sharifi and Taylor has initiated the topic of higher codimension Iwasawa theory. As a generalization of the classical Iwasawa main conjecture, they prove a relationship between analytic objects (a pair of Katz's 2 -variable p -adic L -functions) and algebraic objects (two 'everywhere unramified' Iwasawa modules) involving codimension two cycles in a 2 -variable Iwasawa algebra. We prove a result by considering the restriction to an imaginary quadratic field K (where an odd prime p splits) of an elliptic curve E, defined over Q, with good supersingular reduction at p . On the analytic side, we consider eight pairs of 2 -variable p -adic L -functions in this setup (four of the 2 -variable p -adic L -functions have been constructed by Loeffler and a fifth 2 -variable p -adic L -function is due to Hida). On the algebraic side, we consider modifications of fine Selmer groups over the Z_p^2 -extension of K . We also provide numerical evidence, using algorithms of Pollack, towards a pseudonullity conjecture of Coates–Sujatha.