Supersingular Abelian Varieties Over Finite Fields PDF Download

Author: Hui Zhu
Publisher:
ISBN:
Category :
Languages : en
Pages : 194

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Author: Ke-Zheng Li
Publisher: Springer
ISBN: 3540696660
Category : Mathematics
Languages : en
Pages : 123

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Book Description
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).

Author: Dmitri Kaledin
Publisher: IOS Press
ISBN: 1586038559
Category : Mathematics
Languages : en
Pages : 356

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"Proceedings of the NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields, Geottingen, Germany, 25 June-6 July 2007."--T.p. verso.

Author: Donald J. Lewis
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 476

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Book Description
This book is an outgrowth of the American Mathematical Society's Sixteenth Summer Research Institute, which had as its topics algebraic number theory, Diophantine problems, and analytic number theory. In order to survey the achievements of the decade, the Institute organizing committee invited sixteen speakers to each give a series of lectures. This volume includes the sixteen invited lecture series, and nine seminar talks which present particularly effective surveys of specific areas. These papers are addressed to a general number theory audience rather than specialists, and are meant to enable a number theorist to become acquainted with important innovations in areas outside their own specialties. It is hoped that this collection of papers will facilitate access to various parts of number theory and foster further development.

Author: Igor Shparlinski
Publisher: Springer Science & Business Media
ISBN: 940159239X
Category : Mathematics
Languages : en
Pages : 532

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Book Description
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.

Author: Gerard van der Geer
Publisher: Birkhäuser
ISBN: 303488303X
Category : Mathematics
Languages : en
Pages : 526

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Abelian varieties and their moduli are a topic of increasing importance in today`s mathematics, applications ranging from algebraic geometry and number theory to mathematical physics. This collection of 17 refereed articles originates from the third "Texel Conference" held in 1999. Leading experts discuss and study the structure of the moduli spaces of abelian varieties and related spaces, giving an excellent view of the state of the art in this field.

Author: Goro Shimura
Publisher: Princeton University Press
ISBN: 1400883946
Category : Mathematics
Languages : en
Pages : 232

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Book Description
Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.

Author: Tsuyoshi Takagi
Publisher: Springer Science & Business Media
ISBN: 3540734880
Category : Computers
Languages : en
Pages : 418

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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.

Author: M. Rapoport
Publisher: Princeton University Press
ISBN: 9780691027814
Category : Mathematics
Languages : en
Pages : 350

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Book Description
In this monograph p-adic period domains are associated to arbitrary reductive groups. Using the concept of rigid-analytic period maps the relation of p-adic period domains to moduli space of p-divisible groups is investigated. In addition, non-archimedean uniformization theorems for general Shimura varieties are established. The exposition includes background material on Grothendieck's "mysterious functor" (Fontaine theory), on moduli problems of p-divisible groups, on rigid analytic spaces, and on the theory of Shimura varieties, as well as an exposition of some aspects of Drinfelds' original construction. In addition, the material is illustrated throughout the book with numerous examples.

Author: Hovav Shacham
Publisher: Springer Science & Business Media
ISBN: 3642032974
Category : Computers
Languages : en
Pages : 275

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Book Description
This book constitutes the refereed proceedings of the Third International Conference on Pairing-Based Cryptography, Pairing 2009, held in Palo Alto, CA, USA, in August 2009. The 16 full papers presented were carefully reviewed and selected from 38 submissions. The papers are organized in topical sections on signature security, curves, pairing computation, non-interactive zero-knowledge systems and applications, group signatures, and protocols.