On a construction on p-units in abelian fields.
Canonical factorisations in multiplicative Galois structure.
Some new maps and ideals in classical Iwasawa theory with applications
We introduce a new ideal of the p-adic Galois group-ring associated to a real abelian field and a related ideal for imaginary abelian fields, Both result from an equivariant, Kummer-type pairing applied to Stark units in a -tower of abelian fields, and is linked by explicit reciprocity to a third ideal studied more generally in [D. Solomon, Acta Arith. 143 (2010)]. This leads to a new and unifying framework for the Iwasawa theory of such fields including a real analogue of Stickelberger’s Theorem,...
On the classgroups of imaginary abelian fields
Let be an odd prime, an odd, -adic Dirichlet character and the cyclic imaginary extension of associated to . We define a “-part” of the Sylow -subgroup of the class group of and prove a result relating its -divisibility to that of the generalized Bernoulli number . This uses the results of Mazur and Wiles in Iwasawa theory over . The more difficult case, in which divides the order of is our chief concern. In this case the result is new and confirms an earlier conjecture of G....
-adic Abelian Stark conjectures at
A -adic version of Stark’s Conjecture at is attributed to J.-P. Serre and stated (faultily) in Tate’s book on the Conjecture. Building instead on our previous paper (and work of Rubin) on the complex abelian case, we give a new approach to such a conjecture for real ray-class extensions of totally real number fields. We study the coherence of our -adic conjecture and then formulate some integral refinements, both alone and in combination with its complex analogue. A ‘Weak Combined Refined’ version...
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