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Kato’s main conjecture for potentially ordinary primes

Part of: Arithmetic algebraic geometry Algebraic number theory: global fields

Published online by Cambridge University Press:  26 January 2024

Katharina Müller
Katharina Müller*
Affiliation:
Department of Mathematics and Statistics, Université Laval, Québec City, Canada
*
Email: katharina.mueller.1@ulaval.ca
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Abstract

In this paper, we prove Kato’s main conjecture for $CM$ modular forms for primes of potentially ordinary reduction under certain hypotheses on the modular form.

Keywords

Iwasawa theorymodular formsselmer groupsmain conjecture

MSC classification

Primary: 11G15: Complex multiplication and moduli of abelian varieties 11R23: Iwasawa theory 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 21
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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