eBook ISBN:  9780821877654 
Product Code:  CONM/174.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821877654 
Product Code:  CONM/174.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 174; 1994; 220 ppMSC: Primary 11; Secondary 12
This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with \(p\)adic modular forms of halfintegral weight and their roles in arithmetic geometry. The volume also contains material on the Iwasawa theory of cyclotomic fields, elliptic curves, and function fields, including \(p\)adic \(L\)functions and \(p\)adic height pairings. Other articles focus on the inverse Galois problem, fields of definition of abelian varieties with real multiplication, and computation of torsion groups of elliptic curves. The volume also contains a previously unpublished letter of John Tate, written to J.P. Serre in 1973, concerning Serre's conjecture on Galois representations. With contributions by some of the leading experts in the field, this book provides a look at the state of the art in arithmetic geometry.
ReadershipResearchers and advanced graduate students working in number theory and arithmetic geometry.

Table of Contents

Articles

Michael D. Fried, Dan Haran and Helmut Völklein — Real Hilbertianity and the field of totally real numbers [ MR 1299732 ]

David Harbater — Galois groups with prescribed ramification [ MR 1299733 ]

Tauno Metsänkylä — Note on the zeros of $p$adic $L$functions [ MR 1299734 ]

Bernadette PerrinRiou — La fonction $L$ $p$adique de KubotaLeopoldt [ MR 1299735 ]

Andrew Plater — Supersingular $p$adic height pairings on elliptic curves [ MR 1299736 ]

Kenneth A. Ribet — Fields of definition of abelian varieties with real multiplication [ MR 1299737 ]

Adriana Sofer — $p$adic interpolation of halfintegral weight modular forms [ MR 1299738 ]

Glenn Stevens — $\Lambda $adic modular forms of halfintegral weight and a $\Lambda $adic Shintani lifting [ MR 1299739 ]

John Tate — The nonexistence of certain Galois extensions of ${\bf Q}$ unramified outside $2$ [ MR 1299740 ]

Dinesh S. Thakur — Iwasawa theory and cyclotomic function fields [ MR 1299741 ]

Douglas L. Ulmer — Slopes of modular forms [ MR 1299742 ]

Fernando Rodríguez Villegas — On the Taylor coefficients of theta functions of CM elliptic curves [ MR 1299743 ]

Horst G. Zimmer — Torsion groups of elliptic curves over cubic and certain biquadratic number fields [ MR 1299744 ]


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This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with \(p\)adic modular forms of halfintegral weight and their roles in arithmetic geometry. The volume also contains material on the Iwasawa theory of cyclotomic fields, elliptic curves, and function fields, including \(p\)adic \(L\)functions and \(p\)adic height pairings. Other articles focus on the inverse Galois problem, fields of definition of abelian varieties with real multiplication, and computation of torsion groups of elliptic curves. The volume also contains a previously unpublished letter of John Tate, written to J.P. Serre in 1973, concerning Serre's conjecture on Galois representations. With contributions by some of the leading experts in the field, this book provides a look at the state of the art in arithmetic geometry.
Researchers and advanced graduate students working in number theory and arithmetic geometry.

Articles

Michael D. Fried, Dan Haran and Helmut Völklein — Real Hilbertianity and the field of totally real numbers [ MR 1299732 ]

David Harbater — Galois groups with prescribed ramification [ MR 1299733 ]

Tauno Metsänkylä — Note on the zeros of $p$adic $L$functions [ MR 1299734 ]

Bernadette PerrinRiou — La fonction $L$ $p$adique de KubotaLeopoldt [ MR 1299735 ]

Andrew Plater — Supersingular $p$adic height pairings on elliptic curves [ MR 1299736 ]

Kenneth A. Ribet — Fields of definition of abelian varieties with real multiplication [ MR 1299737 ]

Adriana Sofer — $p$adic interpolation of halfintegral weight modular forms [ MR 1299738 ]

Glenn Stevens — $\Lambda $adic modular forms of halfintegral weight and a $\Lambda $adic Shintani lifting [ MR 1299739 ]

John Tate — The nonexistence of certain Galois extensions of ${\bf Q}$ unramified outside $2$ [ MR 1299740 ]

Dinesh S. Thakur — Iwasawa theory and cyclotomic function fields [ MR 1299741 ]

Douglas L. Ulmer — Slopes of modular forms [ MR 1299742 ]

Fernando Rodríguez Villegas — On the Taylor coefficients of theta functions of CM elliptic curves [ MR 1299743 ]

Horst G. Zimmer — Torsion groups of elliptic curves over cubic and certain biquadratic number fields [ MR 1299744 ]