Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011
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| Sprache: | English |
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Berlin [u.a.]
Springer
2013
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| Schriftenreihe: | Springer proceedings in mathematics and statistics
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Datensatz im Suchindex
| DE-BY-TUM_katkey | 1907472 |
|---|---|
| _version_ | 1816713842613288960 |
| adam_text | NONCOMMUTATIVE IWASAWA MAIN CONJECTURES OVER TOTALLY REAL FIELDS
/
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
JOHN COATES, DOHYEONG KIM: INTRODUCTION TO THE WORK OF M. KAKDE ON THE
NON-COMMUTATIVE MAIN CONJECTURES FOR TOTALLY REAL FIELDS
R. SUJATHA: REDUCTIONS OF THE MAIN CONJECTURE
TED CHINBURG, GEORGIOS PAPPAS, MARTIN J. TAYLOR: THE GROUP LOGARITHM
PAST AND PRESENT
PETER SCHNEIDER, OTMAR VENJAKOB: K_1 OF CERTAIN IWASAWA ALGEBRAS,
AFTER KAKDE
MAHESH KAKDE: CONGRUENCES BETWEEN ABELIAN P-ADIC ZETA FUNCTIONS
OTMAR VENJAKOB: ON THE WORK OF RITTER AND WEISS IN COMPARISON WITH
KAKDE S APPROACH
MALTE WITTE: NONCOMMUTATIVE MAIN CONJECTURES OF GEOMETRIC IWASAWA
THEORY
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
NONCOMMUTATIVE IWASAWA MAIN CONJECTURES OVER TOTALLY REAL FIELDS
/
: 2013
ABSTRACT / INHALTSTEXT
THE ALGEBRAIC TECHNIQUES DEVELOPED BY KAKDE WILL ALMOST CERTAINLY LEAD
EVENTUALLY TO MAJOR PROGRESS IN THE STUDY OF CONGRUENCES BETWEEN
AUTOMORPHIC FORMS AND THE MAIN CONJECTURES OF NON-COMMUTATIVE IWASAWA
THEORY FOR MANY MOTIVES. NON-COMMUTATIVE IWASAWA THEORY HAS EMERGED
DRAMATICALLY OVER THE LAST DECADE, CULMINATING IN THE RECENT PROOF OF
THE NON-COMMUTATIVE MAIN CONJECTURE FOR THE TATE MOTIVE OVER A TOTALLY
REAL P-ADIC LIE EXTENSION OF A NUMBER FIELD, INDEPENDENTLY BY RITTER AND
WEISS ON THE ONE HAND, AND KAKDE ON THE OTHER. THE INITIAL IDEAS FOR
GIVING A PRECISE FORMULATION OF THE NON-COMMUTATIVE MAIN CONJECTURE WERE
DISCOVERED BY VENJAKOB, AND WERE THEN SYSTEMATICALLY DEVELOPED IN THE
SUBSEQUENT PAPERS BY COATES-FUKAYA-KATO-SUJATHA-VENJAKOB AND
FUKAYA-KATO. THERE WAS ALSO PARALLEL RELATED WORK IN THIS DIRECTION BY
BURNS AND FLACH ON THE EQUIVARIANT TAMAGAWA NUMBER CONJECTURE.
SUBSEQUENTLY, KATO DISCOVERED AN IMPORTANT IDEA FOR STUDYING THE K_1
GROUPS OF NON-ABELIAN IWASAWA ALGEBRAS IN TERMS OF THE K_1 GROUPS OF THE
ABELIAN QUOTIENTS OF THESE IWASAWA ALGEBRAS. KAKDE S PROOF IS A
BEAUTIFUL DEVELOPMENT OF THESE IDEAS OF KATO, COMBINED WITH AN IDEA OF
BURNS, AND ESSENTIALLY REDUCES THE STUDY OF THE NON-ABELIAN MAIN
CONJECTURES TO ABELIAN ONES. THE APPROACH OF RITTER AND WEISS IS MORE
CLASSICAL, AND PARTLY INSPIRED BY TECHNIQUES OF FROHLICH AND TAYLOR.
SINCE MANY OF THE IDEAS IN THIS BOOK SHOULD EVENTUALLY BE APPLICABLE TO
OTHER MOTIVES, ONE OF ITS MAJOR AIMS IS TO PROVIDE A SELF-CONTAINED
EXPOSITION OF SOME OF THE MAIN GENERAL THEMES UNDERLYING THESE
DEVELOPMENTS. THE PRESENT VOLUME WILL BE A VALUABLE RESOURCE FOR
RESEARCHERS WORKING IN BOTH IWASAWA THEORY AND THE THEORY OF AUTOMORPHIC
FORMS.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| language | English |
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| publishDate | 2013 |
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| publisher | Springer |
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| series2 | Springer proceedings in mathematics and statistics |
| spellingShingle | Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011 Iwasawa-Theorie (DE-588)4384573-3 gnd |
| subject_GND | (DE-588)4384573-3 (DE-588)1071861417 |
| title | Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011 |
| title_auth | Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011 |
| title_exact_search | Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011 |
| title_full | Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011 John Coates ..., ed. |
| title_fullStr | Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011 John Coates ..., ed. |
| title_full_unstemmed | Noncommutative Iwasawa main conjectures over totally real fields Münster, April 2011 John Coates ..., ed. |
| title_short | Noncommutative Iwasawa main conjectures over totally real fields |
| title_sort | noncommutative iwasawa main conjectures over totally real fields munster april 2011 |
| title_sub | Münster, April 2011 |
| topic | Iwasawa-Theorie (DE-588)4384573-3 gnd |
| topic_facet | Iwasawa-Theorie Konferenzschrift 2011 Münster |
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