Fitting ideals of p-ramified Iwasawa modules over totally real fields

Cornelius Greither; Takenori Kataoka; Masato Kurihara

doi:10.1007/s00029-021-00731-5

Fitting ideals of p-ramified Iwasawa modules over totally real fields

Cornelius Greither, Takenori Kataoka, Masato Kurihara

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We completely calculate the Fitting ideal of the classical p-ramified Iwasawa module for any abelian extension K/k of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former results where we had to assume that only p-adic places may ramify in K/k. One of the important ingredients is the computation of some complexes in appropriate derived categories.

Original language	English
Article number	14
Journal	Selecta Mathematica, New Series
Volume	28
Issue number	1
DOIs	https://doi.org/10.1007/s00029-021-00731-5
Publication status	Published - 2022 Feb

Keywords

Cohomology
Complexes
Fitting ideals
Iwasawa modules

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)

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10.1007/s00029-021-00731-5

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title = "Fitting ideals of p-ramified Iwasawa modules over totally real fields",

abstract = "We completely calculate the Fitting ideal of the classical p-ramified Iwasawa module for any abelian extension K/k of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former results where we had to assume that only p-adic places may ramify in K/k. One of the important ingredients is the computation of some complexes in appropriate derived categories.",

keywords = "Cohomology, Complexes, Fitting ideals, Iwasawa modules",

author = "Cornelius Greither and Takenori Kataoka and Masato Kurihara",

note = "Funding Information: The second-named author acknowledges support by JSPS KAKENHI Grant Number 19J00763. Publisher Copyright: {\textcopyright} 2021, The Author(s).",

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AU - Kataoka, Takenori

AU - Kurihara, Masato

PY - 2022/2

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N2 - We completely calculate the Fitting ideal of the classical p-ramified Iwasawa module for any abelian extension K/k of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former results where we had to assume that only p-adic places may ramify in K/k. One of the important ingredients is the computation of some complexes in appropriate derived categories.

AB - We completely calculate the Fitting ideal of the classical p-ramified Iwasawa module for any abelian extension K/k of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former results where we had to assume that only p-adic places may ramify in K/k. One of the important ingredients is the computation of some complexes in appropriate derived categories.

KW - Cohomology

KW - Complexes

KW - Fitting ideals

KW - Iwasawa modules

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Fitting ideals of p-ramified Iwasawa modules over totally real fields

Abstract

Keywords

ASJC Scopus subject areas

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