p-adic L-functions and p-adic representations / Bernadette Perrin-Riou ; translated by Leila Schneps.

Format:

Book

Author/Creator:

Perrin-Riou, Bernadette.

Series:

SMF/AMS texts and monographs 1525-2302 ; v. 3.

SMF/AMS texts and monographs, 1525-2302 ; v. 3

Standardized Title:

Fonctions L p-adiques des représentations p-adiques. English

Language:

English

French

Subjects (All):

L-functions.

p-adic numbers.

Algebraic number theory.

Physical Description:

xx, 150 pages ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society ; [Paris] : Société Mathématique de France, [2000]

Contents:

Chapter 1. Construction of the module of p-adic L-functions without factors at infinity 1

1.1. Notation 3

1.2. Study of some local [Lambda]-modules 5

1.3. Galois cohomology 10

1.4. The module of p-adic L-functions (without factors at infinity) 13

Chapter 2. Modules of p-adic L-functions of V 19

2.1. [Gamma]-factors 21

2.2. The module of p-adic L-functions 27

2.3. Some properties 29

2.4. Relations with the usual characteristic series and examples 30

2.5. The functional equation 36

Chapter 3. Values of the module of p-adic L-functions 41

3.1. p-adic periods 43

3.2. Examples and special cases 50

3.3. Multiplicity of the zero (first form) 52

3.4. Multiplicity of the zero (second form) 57

3.5. Special values and periods 67

3.6. Special values 71

Chapter 4. The p-adic L-function of a motive 79

4.2. Conjectural definition of the p-adic L-function of a motive 85

4.3. Remarks and examples 90

4.4. Special elements 106

4.5. Continuity 111

Appendix A. Results in Galois cohomology 115

A.1. Galois cohomology 115

A.2. Local Iwasawa theory: first results 118

A.3. Poitou-Tate exact sequences 121

A.4. Iwasawa theory and twists 123

Appendix B. The weak Leopoldt conjecture 125

Appendix C. Local Tamagawa numbers and Euler-Poincare characteristic. Application to the functional equation 131

C.1. Local factors and [epsilon] factors: the non-Archimedean case 133

C.2. Local Euler-Poincare characteristic 135

C.3. Compatibility of the Bloch-Kato conjectures with the functional equation 140.

Notes:

Includes bibliographical references (pages 143-146) and index.

ISBN:

0821819461

OCLC:

42761957