Some new maps and ideals in classical Iwasawa theory with applications

• Autorzy: David Solomon
• Języki publikacji: EN

Abstrakty

EN

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 [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 Λ-torsion submodules, and a new exact sequence related to the Main Conjecture.

Kategorie tematyczne

• 11R42: Zeta functions and L -functions of number fields
• 11R18: Cyclotomic extensions
• 11R23: Iwasawa theory
• 11R29: Class numbers, class groups, discriminants
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 2
• Strony: 101-140

Daty

wydano

2014

Twórcy

autor

David Solomon

• 132 Hillfield Ave., London N8 7DJ, United Kingdom

Identyfikatory

DOI

10.4064/aa162-2-1