IWASAWA THEORY FOR ONE-PARAMETER FAMILIES OF MOTIVES

Abstract

In [A formulation of conjectures on p-adic zeta functions in non-commutative Iwasawa theory, in Proc. St. Petersburg Mathematical Society, Vol. 12, American Mathematical Society Translations, Series 2, Vol. 219 (American Mathematical Society, Providence, RI, 2006), pp. 1–85] Fukaya and Kato presented equivariant Tamagawa number conjectures that implied a very general (non-commutative) Iwasawa main conjecture for rather general motives. In this article we apply their methods to the case of one-parameter families of motives to derive a main conjecture for such families. On our way there we get some unconditional results on the variation of the (algebraic) λ- and μ-invariant. We focus on the results dealing with Selmer complexes instead of the more classical notion of Selmer groups. However, where possible we give the connection to the classical notions.