Let p be an odd prime number. We prove the existence of certain infinite families of imaginary quadratic fields in which p splits and for which the Iwasawa λ-invariant of the cyclotomic ℤₚ-extension is equal to 1.
We give precise estimates for the number of classical weight one specializations of a non-CM family of ordinary cuspidal eigenforms. We also provide examples to show how uniqueness fails with respect to membership of weight one forms in families.
We present a collection of results on a conjecture of Jannsen about the p-adic realizations associated to Hecke characters over an imaginary quadratic field K of class number 1.The conjecture is easy to check for Galois groups purely of local type (Section 1). In Section 2 we define the p-adic realizations associated to Hecke characters over K. We prove the conjecture under a geometric regularity condition for the imaginary quadratic field K at p, which is related to the property that a global Galois...
This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups , where is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.