PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Some new maps and ideals in classical Iwasawa theory with applications

Volume 162 / 2014

David Solomon Acta Arithmetica 162 (2014), 101-140 MSC: Primary 11R18, 11R23; Secondary 11R27, 11R29, 11R42. DOI: 10.4064/aa162-2-1


We introduce a new ideal $ {\mathfrak {D}}$ of the $p$-adic Galois group-ring associated to a real abelian field and a related ideal $ {\mathfrak {J}}$ for imaginary abelian fields, Both result from an equivariant, Kummer-type pairing applied to Stark units in a $ {\mathbb {Z}}_p$-tower of abelian fields, and $ {\mathfrak {J}}$ is linked by explicit reciprocity to a third ideal $ {\mathfrak {S}}$ 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, links with certain Fitting ideals and $\varLambda $-torsion submodules, and a new exact sequence related to the Main Conjecture.


  • David Solomon132 Hillfield Ave.
    London N8 7DJ, United Kingdom

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image