Some new maps and ideals in classical Iwasawa theory with applications

David Solomon. "Some new maps and ideals in classical Iwasawa theory with applications." Acta Arithmetica 162.2 (2014): 101-140. <http://eudml.org/doc/279016>.

@article{DavidSolomon2014,
abstract = {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 $ℤ_p$-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, links with certain Fitting ideals and Λ-torsion submodules, and a new exact sequence related to the Main Conjecture.},
author = {David Solomon},
journal = {Acta Arithmetica},
keywords = {Iwasawa theory; Kummer theory; abelian field; cylcotomic units; class group},
language = {eng},
number = {2},
pages = {101-140},
title = {Some new maps and ideals in classical Iwasawa theory with applications},
url = {http://eudml.org/doc/279016},
volume = {162},
year = {2014},
}

TY - JOUR
AU - David Solomon
TI - Some new maps and ideals in classical Iwasawa theory with applications
JO - Acta Arithmetica
PY - 2014
VL - 162
IS - 2
SP - 101
EP - 140
AB - 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 $ℤ_p$-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, links with certain Fitting ideals and Λ-torsion submodules, and a new exact sequence related to the Main Conjecture.
LA - eng
KW - Iwasawa theory; Kummer theory; abelian field; cylcotomic units; class group
UR - http://eudml.org/doc/279016
ER -