Iwasawa Theory and Its Perspective, Volume 2
Seiten
2024
American Mathematical Society (Verlag)
978-1-4704-5673-3 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5673-3 (ISBN)
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Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to ??-adic ??-functions. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory.
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory.
The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory.
The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
Tadashi Ochiai, Tokyo Institute of Technology, Japan.
Introduction to cyclotomic Iwasawa theory of elliptic curves
Framework of cyclotomic Iwasawa theory for $p$-adic Galois representations
Known results on cyclotomic Iwasawa theory for $p$-adic representations
Appendix A
| Erscheinungsdatum | 15.05.2024 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs ; 280 |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-5673-7 / 1470456737 |
| ISBN-13 | 978-1-4704-5673-3 / 9781470456733 |
| Zustand | Neuware |
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