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$p$-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture
 
Edited by: Barry Mazur :  Harvard University, Cambridge, MA
Glenn Stevens :  Boston University, Boston, MA
$p$-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture
eBook ISBN:  978-0-8218-7756-2
Product Code:  CONM/165.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
$p$-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture
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$p$-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture
Edited by: Barry Mazur :  Harvard University, Cambridge, MA
Glenn Stevens :  Boston University, Boston, MA
eBook ISBN:  978-0-8218-7756-2
Product Code:  CONM/165.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 165; 1994; 315 pp
    MSC: Primary 11; Secondary 14

    Recent years have witnessed significant breakthroughs in the theory of \(p\)-adic Galois representations and \(p\)-adic periods of algebraic varieties. This book contains papers presented at the Workshop on \(p\)-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, held at Boston University in August 1991. The workshop aimed to deepen understanding of the interdependence between \(p\)-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, \(p\)-adic uniformization theory, \(p\)-adic differential equations, and deformations of Galois representations. Much of the workshop was devoted to exploring how the special values of (\(p\)-adic and “classical”) \(L\)-functions and their derivatives are relevant to arithmetic issues, as envisioned in “Birch-Swinnerton-Dyer-type conjectures”, “Main Conjectures”, and “Beilinson-type conjectures” à la Greenberg and Coates.
    Readership

    Research mathematicians.
  • Table of Contents
     
     
    • Articles
    • B. Mazur — On monodromy invariants occurring in global arithmetic, and Fontaine’s theory [ MR 1279599 ]
    • Robert F. Coleman — A $p$-adic Shimura isomorphism and $p$-adic periods of modular forms [ MR 1279600 ]
    • Robert Coleman and Jeremy Teitelbaum — Numerical solution of the $p$-adic hypergeometric equation [ MR 1279601 ]
    • John W. Jones — Iwasawa $L$-functions and the mysterious ${\scr L}$-invariant [ MR 1279602 ]
    • Karl Rubin — $p$-adic variants of the Birch and Swinnerton-Dyer conjecture for elliptic curves with complex multiplication [ MR 1279603 ]
    • Koji Kitagawa — On standard $p$-adic $L$-functions of families of elliptic cusp forms [ MR 1279604 ]
    • Ki-Seng Tan — $p$-adic pairings [ MR 1279605 ]
    • Joseph H. Silverman — Variation of the canonical height in algebraic families [ MR 1279606 ]
    • Ehud de Shalit — Kronecker’s polynomial, supersingular elliptic curves, and $p$-adic periods of modular curves [ MR 1279607 ]
    • Ralph Greenberg — Trivial zeros of $p$-adic $L$-functions [ MR 1279608 ]
    • Bruce W. Jordan — Higher weight modular forms and Galois representations [ MR 1279609 ]
    • Ralph Greenberg and Glenn Stevens — On the conjecture of Mazur, Tate, and Teitelbaum [ MR 1279610 ]
    • Henri Carayol — Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet [ MR 1279611 ]
    • Naomi Jochnowitz — A $p$-adic conjecture about derivatives of $L$-series attached to modular forms [ MR 1279612 ]
    • Henri Darmon — Euler systems and refined conjectures of Birch Swinnerton-Dyer type [ MR 1279613 ]
    • Christoph Klingenberg — On $p$-adic $L$-functions of Mumford curves [ MR 1279614 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Contemporary Mathematics
Volume: 165; 1994; 315 pp
MSC: Primary 11; Secondary 14

Recent years have witnessed significant breakthroughs in the theory of \(p\)-adic Galois representations and \(p\)-adic periods of algebraic varieties. This book contains papers presented at the Workshop on \(p\)-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, held at Boston University in August 1991. The workshop aimed to deepen understanding of the interdependence between \(p\)-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, \(p\)-adic uniformization theory, \(p\)-adic differential equations, and deformations of Galois representations. Much of the workshop was devoted to exploring how the special values of (\(p\)-adic and “classical”) \(L\)-functions and their derivatives are relevant to arithmetic issues, as envisioned in “Birch-Swinnerton-Dyer-type conjectures”, “Main Conjectures”, and “Beilinson-type conjectures” à la Greenberg and Coates.
Readership

Research mathematicians.
  • Articles
  • B. Mazur — On monodromy invariants occurring in global arithmetic, and Fontaine’s theory [ MR 1279599 ]
  • Robert F. Coleman — A $p$-adic Shimura isomorphism and $p$-adic periods of modular forms [ MR 1279600 ]
  • Robert Coleman and Jeremy Teitelbaum — Numerical solution of the $p$-adic hypergeometric equation [ MR 1279601 ]
  • John W. Jones — Iwasawa $L$-functions and the mysterious ${\scr L}$-invariant [ MR 1279602 ]
  • Karl Rubin — $p$-adic variants of the Birch and Swinnerton-Dyer conjecture for elliptic curves with complex multiplication [ MR 1279603 ]
  • Koji Kitagawa — On standard $p$-adic $L$-functions of families of elliptic cusp forms [ MR 1279604 ]
  • Ki-Seng Tan — $p$-adic pairings [ MR 1279605 ]
  • Joseph H. Silverman — Variation of the canonical height in algebraic families [ MR 1279606 ]
  • Ehud de Shalit — Kronecker’s polynomial, supersingular elliptic curves, and $p$-adic periods of modular curves [ MR 1279607 ]
  • Ralph Greenberg — Trivial zeros of $p$-adic $L$-functions [ MR 1279608 ]
  • Bruce W. Jordan — Higher weight modular forms and Galois representations [ MR 1279609 ]
  • Ralph Greenberg and Glenn Stevens — On the conjecture of Mazur, Tate, and Teitelbaum [ MR 1279610 ]
  • Henri Carayol — Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet [ MR 1279611 ]
  • Naomi Jochnowitz — A $p$-adic conjecture about derivatives of $L$-series attached to modular forms [ MR 1279612 ]
  • Henri Darmon — Euler systems and refined conjectures of Birch Swinnerton-Dyer type [ MR 1279613 ]
  • Christoph Klingenberg — On $p$-adic $L$-functions of Mumford curves [ MR 1279614 ]
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