Resumen de Control theorem and functional equation of Selmer groups over p-adic Lie extensions
Somnath Jha, Tadashi Ochiai
Let K∞ be a p-adic Lie extension of a number field K which fits into the setting of non-commutative Iwasawa theory formulated by Coates–Fukaya–Kato–Sujatha–Venjakob. For the first main result, we will prove the control theorem of Selmer group associated to a motive, which generalizes previous results by the second author and Greenberg. As an application of this control theorem, we prove the functional equation of the dual Selmer groups, which generalizes previous results by Greenberg, Perrin-Riou and Zábrádi. Especially, we generalize the result of Zábrádi for elliptic curves to general motives. Note that our proof is different from the proof of Zábrádi even in the case of elliptic curves. We also discuss the functional equation for the analytic p-adic L-functions and check the compatibility with the functional equation of the dual Selmer groups.
