Supersingular Abelian Varieties Over Finite Fields
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Supersingular Abelian Varieties Over Finite Fields
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Author : Hui Zhu
language : en
Publisher:
Release Date : 1997
Supersingular Abelian Varieties Over Finite Fields written by Hui Zhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Moduli Of Supersingular Abelian Varieties
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Author : Ke-Zheng Li
language : en
Publisher: Springer
Release Date : 2006-11-14
Moduli Of Supersingular Abelian Varieties written by Ke-Zheng Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).
Higher Dimensional Geometry Over Finite Fields
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Author : Dmitri Kaledin
language : en
Publisher: IOS Press
Release Date : 2008
Higher Dimensional Geometry Over Finite Fields written by Dmitri Kaledin and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"Proceedings of the NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields, Geottingen, Germany, 25 June-6 July 2007."--T.p. verso.
Public Record Office
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Author :
language : en
Publisher:
Release Date : 1994
Public Record Office written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Finite Fields Theory And Computation
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Author : Igor Shparlinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Finite Fields Theory And Computation written by Igor Shparlinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.
Geometry Over Nonclosed Fields
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Author : Fedor Bogomolov
language : en
Publisher: Springer
Release Date : 2017-02-09
Geometry Over Nonclosed Fields written by Fedor Bogomolov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-09 with Mathematics categories.
Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
Moduli Of Curves And Abelian Varieties
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Author : Carel Faber
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Moduli Of Curves And Abelian Varieties written by Carel Faber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Rain, E. Looijenga, and F. Oort, originates from the Dutch Intercity Seminar on Moduli (year 1995-96). Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles. Topics include a stratification of a moduli space of abelian varieties in positive characteristic, and the calculation of the classes of the strata, tautological classes for moduli of abelian varieties as well as for moduli of curves, correspondences between moduli spaces of curves, locally symmetric families of curves and jaco bians, and the role of symmetric product spaces in quantum field theory, string theory and matrix theory. This Intercity Seminar is part of the long term project "Algebraic curves and Riemann surfaces: geometry, arithmetic and applications" , sponsored hy the Netherlands Organization for Scientific Research (NWO), that has been running since 1994. Its ancestry can be traced back to joint activities in the seventies (if not earlier), which as of 1980 had evolved into active biweekly research seminars. These have been a focal point of Dutch algebraic geometry and singularity theory since. We are grateful to NWO for its support for the project. C.F. thanks the Max-Planck-Institut fur Mathematik, Bonn, for support during the final stages of the preparation of this volume.
Progress In Cryptology Indocrypt 2005
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Author : C.E. Veni Madhavan
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-24
Progress In Cryptology Indocrypt 2005 written by C.E. Veni Madhavan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-24 with Business & Economics categories.
This book constitutes the refereed proceedings of the 6th International Conference on Cryptology in India, INDOCRYPT 2005, held in Bangalore, India in December 2005. The 31 revised full papers presented together with 1 invited paper were carefully reviewed and selected from 148 submissions. The papers are organized in topical sections on sequences, boolean function and S-box, hash functions, design principles, cryptanalysis, time memory trade-off, new constructions, pairings, signatures, applications, e-cash, and implementations.
Pairing Based Cryptography Pairing 2007
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Author : Tsuyoshi Takagi
language : en
Publisher: Springer
Release Date : 2007-09-12
Pairing Based Cryptography Pairing 2007 written by Tsuyoshi Takagi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-12 with Computers categories.
Pairing-based cryptography is at the very leading edge of the current wave in computer cryptography. That makes this book all the more relevant, being as it is the refereed proceedings of the First International Conference on Pairing-Based Cryptography, Pairing 2007, held in Tokyo, Japan in 2007. The 18 revised full papers presented together were carefully reviewed and selected from 86 submissions. The papers are organized in topical sections including those on applications, and certificateless public key encryption.
The Arithmetic And Geometry Of Algebraic Cycles
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Author : B. Brent Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
The Arithmetic And Geometry Of Algebraic Cycles written by B. Brent Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The NATO ASI/CRM Summer School at Banff offered a unique, full, and in-depth account of the topic, ranging from introductory courses by leading experts to discussions of the latest developments by all participants. The papers have been organized into three categories: cohomological methods; Chow groups and motives; and arithmetic methods.As a subfield of algebraic geometry, the theory of algebraic cycles has gone through various interactions with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to developments such as a description of Chow groups in terms of algebraic K-theory, the application of the Merkurjev-Suslin theorem to the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge, and of Tate, which compute cycles classgroups respectively in terms of Hodge theory or as the invariants of a Galois group action on étale cohomology, the conjectures of Bloch and Beilinson, which explain the zero or pole of the $L$-function of a variety and interpret the leading non-zero coefficient of its Taylor expansion at a criticalpoint, in terms of arithmetic and geometric invariant of the variety and its cycle class groups.The immense recent progress in the theory of algebraic cycles is based on its many interactions with several other areas of mathematics. This conference was the first to focus on both arithmetic and geometric aspects of algebraic cycles. It brought together leading experts to speak from their various points of view. A unique opportunity was created to explore and view the depth and the breadth of the subject. This volume presents the intriguing results.