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p-adic differential equations

p-adic differential equations (2회 대출)

자료유형
단행본
개인저자
Kedlaya, Kiran Sridhara, 1974-.
서명 / 저자사항
p-adic differential equations / Kiran S. Kedlaya.
발행사항
Cambridge ;   New York :   Cambridge University Press,   2010.  
형태사항
xvii, 380 p. : ill. ; 24 cm.
총서사항
Cambridge studies in advanced mathematics ;125
ISBN
9780521768795 (hardback)
요약
"Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study"--Provided by publisher.
내용주기
Norms on algebraic structures -- Newton polygons -- Ramification theory -- Matrix analysis -- Formalism of differential algebra -- Metric properties of differential modules -- Regular singularities -- Rings of functions on discs and annuli -- Radius and generic radius of convergence -- Frobenius pullback and pushforward -- Variation of generic and subsidiary radii -- Decomposition by subsidiary radii -- p-adic exponents -- Formalism of difference algebra -- Frobenius modules -- Frobenius modules over the Robba ring -- Frobenius structures on differential modules -- Effective convergence bounds -- Galois representations and differential modules -- The p-adic local monodromy theorem -- The p-adic local monodromy theorem: proof -- Picard-Fuchs modules -- Rigid cohomology -- p-adic Hodge theory.
서지주기
Includes bibliographical references and index.
일반주제명
p-adic analysis. Differential equations.
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010 ▼a 2010004489
015 ▼a GBB039433 ▼2 bnb
020 ▼a 9780521768795 (hardback)
035 ▼a (OCoLC)ocn503072990
040 ▼a DLC ▼c DLC ▼d YDX ▼d BTCTA ▼d UKM ▼d YDXCP ▼d BWK ▼d CDX ▼d BWX ▼d IXA ▼d IUL ▼d DLC ▼d 211009
050 0 0 ▼a QA241 ▼b .K43 2010
082 0 0 ▼a 512.7/4 ▼2 22
084 ▼a 512.74 ▼2 DDCK
090 ▼a 512.74 ▼b K25p
100 1 ▼a Kedlaya, Kiran Sridhara, ▼d 1974-.
245 1 0 ▼a p-adic differential equations / ▼c Kiran S. Kedlaya.
260 ▼a Cambridge ; ▼a New York : ▼b Cambridge University Press, ▼c 2010.
300 ▼a xvii, 380 p. : ▼b ill. ; ▼c 24 cm.
490 1 ▼a Cambridge studies in advanced mathematics ; ▼v 125
504 ▼a Includes bibliographical references and index.
505 0 ▼a Norms on algebraic structures -- Newton polygons -- Ramification theory -- Matrix analysis -- Formalism of differential algebra -- Metric properties of differential modules -- Regular singularities -- Rings of functions on discs and annuli -- Radius and generic radius of convergence -- Frobenius pullback and pushforward -- Variation of generic and subsidiary radii -- Decomposition by subsidiary radii -- p-adic exponents -- Formalism of difference algebra -- Frobenius modules -- Frobenius modules over the Robba ring -- Frobenius structures on differential modules -- Effective convergence bounds -- Galois representations and differential modules -- The p-adic local monodromy theorem -- The p-adic local monodromy theorem: proof -- Picard-Fuchs modules -- Rigid cohomology -- p-adic Hodge theory.
520 ▼a "Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study"--Provided by publisher.
520 ▼a "Although the very existence of a highly developed theory of p-adic ordinary differential equations is not entirely well known even within number theory, the subject is actually almost 50 years old. Here are circumstances, past and present, in which it arises"-- Provided by publisher.
650 0 ▼a p-adic analysis.
650 0 ▼a Differential equations.
830 0 ▼a Cambridge studies in advanced mathematics ; ▼v 125.
945 ▼a KLPA

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.74 K25p 등록번호 121200316 도서상태 대출중 반납예정일 2023-04-25 예약 예약가능 R 서비스 M

컨텐츠정보

목차

Preface; Introductory remarks; Part I. Tools of p-adic Analysis: 1. Norms on algebraic structures; 2. Newton polygons; 3. Ramification theory; 4. Matrix analysis; Part II. Differential Algebra: 5. Formalism of differential algebra; 6. Metric properties of differential modules; 7. Regular singularities; Part III. p-adic Differential Equations on Discs and Annuli: 8. Rings of functions on discs and annuli; 9. Radius and generic radius of convergence; 10. Frobenius pullback and pushforward; 11. Variation of generic and subsidiary radii; 12. Decomposition by subsidiary radii; 13. p-adic exponents; Part IV. Difference Algebra and Frobenius Modules: 14. Formalism of difference algebra; 15. Frobenius modules; 16. Frobenius modules over the Robba ring; Part V. Frobenius Structures: 17. Frobenius structures on differential modules; 18. Effective convergence bounds; 19. Galois representations and differential modules; 20. The p-adic local monodromy theorem: Statement; 21. The p-adic local monodromy theorem: Proof; Part VI. Areas of Application: 22. Picard-Fuchs modules; 23. Rigid cohomology; 24. p-adic Hodge theory; References; Index of notation; Index.


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