Zp-Extensions of complex multiplication fields

Zp-Extensions of Totally Real Fields

We continue our investigations into complex and p-adic variants of H. M. Stark’s conjectures [St] for an abelian extension of number fields K/k. We have formulated versions of these conjectures at s = 1 using so-called ‘twisted zeta-functions’ (attached to additive characters) to replace the more usual L-functions. The complex version of the conjecture was given in [So3]. In [So4] we formulated...

Zp-Extensions of Imaginary Quadratic Fields

UNRAMIFIED EXTENSIONS AND GEOMETRIC Zp-EXTENSIONS OF GLOBAL FUNCTION FIELDS

We study on finite unramified extensions of global function fields (function fields of one valuable over a finite field). We show two results. One is an extension of Perret’s result about the ideal class group problem. Another is a construction of a geometric Zp-extension which has a certain property.

Iwasawa Theory of Zp-Extensions over Global Function Fields

In this paper we study the Iwasawa theory of Zp-extensions of global function fields k over finite fields of characteristic p. When d = 1 we first show that Iwasawa invariants are well defined under the assumption that only finitely many primes are ramified in the extension, then we prove that the Iwasawa μ-invariant can be arbitrarily large for some extension of any given base field k. After g...

SPINOR GENERA UNDER Zp-EXTENSIONS

Let L be a quadratic lattice over a number field F . We lift the lattice L along a Zp-extension of F and investigate the growth of the number of spinor genera in the genus of L. Let Ln be the lattice obtained from L by extending scalars to the n-th layer of the Zp-extension. We show that, under various conditions on L and F , the number of spinor genera in the genus of Ln is 2 +O(1) where η is ...