The Main Conjecture of Iwasawa theory for an elliptic curve E over Q and the anticyclotomic Zp-extension of an imaginary quadratic field K was studied in [BD2], in the case where p is a prime of ordinary reduction for E. Analogous results are formulated, and proved, in the case where p is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by...

We introduce a new ideal D of the p-adic Galois group-ring associated to a real abelian field and a related ideal J for imaginary abelian fields. Both result from an equivariant, Kummer-type pairing applied to Stark units in a Z p-tower of abelian fields and J is linked by explicit reciprocity to a third ideal S studied more generally in [So3]. This leads to a new and unifying framework for the...

1.1. The Iwasawa-Greenberg Main Conjecture. Let p be an odd prime. Let Q ⊂ C be the algebraic closure of Q in C. We fix an embedding Q ↪→ Qp. For simplicity we also fix an isomorphism Qp ∼= C compatible with the inclusion of Q into both. We let Q∞ be the cyclotomic Zp-extension of Q and ΓQ := Gal(Q∞/Q) its Galois group. The reciprocity map of class field theory identifies 1 + pZp with ΓQ; we le...

This article is concerned with proving a refined function field analogue of the Coates-Sinnott conjecture, formulated in the number field context in 1974. Our main theorem calculates the Fitting ideal of a certain even Quillen K-group in terms of special values of L-functions. The techniques employed are directly inspired by recent work of Greither and Popescu in the equivariant Iwasawa theory ...

We provide a relation between the $\mu $-invariants of dual plus and minus Selmer groups for supersingular elliptic curves when we ascend from cyclotomic ${\mathbb Z}_p$-extension to Z}_p^2$-extension over an imaginary quadratic field.

For a usual local field of mixed characteristic (0, p), we have the theory of Coleman power series [Co]. By applying this theory to the norm compatible system of cyclotomic elements, we obtain the p-adic Riemann zeta function of Kubota-Leopoldt [KL]. This application is very important in cyclotomic Iwasawa theory. In [Fu1], the author defined and studied Coleman power series for K2 for certain ...

Let E/Q be an elliptic curve and let p be an odd supersingular prime for E. In this article, we study the simplest case of Iwasawa theory for elliptic curves, namely when E(Q) is finite, X(E/Q) has no p-torsion and the Tamagawa factors for E are all prime to p. Under these hypotheses, we prove that E(Qn) is finite and make precise statements about the size and structure of the p-power part of X...