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008 170811s2017 riu ob 001 0 eng d;

020 a| 9781470440893q| (electronic bk.);

020 a| 147044089Xq| (electronic bk.);

020 z| 9781470436230;

020 z| 147043623X;

035 a| (Sirsi) o1000357453;

035 a| (OCoLC)1000357453;

049 a| EREE;

050 4 a| QA641b| .B774 2017eb;

072 7 a| MATx| 0120002| bisacsh;

082 04 a| 516.36;

084 a| 11E57a| 11F85a| 14G20a| 53C212| msc;

100 1 a| Buium, Alexandru,d| 1955-e| author.=| ^A193889;

245 10 a| Foundations of arithmetic differential geometry /c| Alexandru Buium.;

264 1 a| Providence, Rhode Island :b| American Mathematical Society,c| [2017];

300 a| 1 online resource.;

336 a| text2| rdacontent;

337 a| computer2| rdamedia;

338 a| online resource2| rdacarrier;

490 1 a| Mathematical surveys and monographs ;v| volume 222;

505 0 a| Cover; Title page; Contents; Preface; Acknowledgments; Introduction; 0.1. Outline of the theory; 0.2. Comparison with other theories; Chapter 1. Algebraic background; 1.1. Algebra; 1.2. Algebraic geometry; 1.3. Superalgebra; Chapter 2. Classical differential geometry revisited; 2.1. Connections in principal bundles and curvature; 2.2. Lie algebra and classical groups; 2.3. Involutions and symmetric spaces; 2.4. Logarithmic derivative and differential Galois groups; 2.5. Chern connections: the symmetric/anti-symmetric case; 2.6. Chern connections: the hermitian case;

505 8 a| 2.7. Levi-Cività connection and Fedosov connection; 2.8. Locally symmetric connections; 2.9. Ehresmann connections attached to inner involutions; 2.10. Connections in vector bundles; 2.11. Lax connections; 2.12. Hamiltonian connections; 2.13. Cartan connection; 2.14. Weierstrass and Riccati connections; 2.15. Differential groups: Cassidy and Painlevé; Chapter 3. Arithmetic differential geometry: generalities; 3.1. Global connections and their curvature; 3.2. Adelic connections; 3.3. Semiglobal connections and their curvature; Galois connections;

505 8 a| 3.4. Curvature via analytic continuation between primes; 3.5. Curvature via algebraization by correspondences; 3.6. Arithmetic jet spaces and the Cartan connection; 3.7. Arithmetic Lie algebras and arithmetic logarithmic derivative; 3.8. Compatibility with translations and involutions; 3.9. Arithmetic Lie brackets and exponential; 3.10. Hamiltonian formalism and Painlevé; 3.11. -adic connections on curves: Weierstrass and Riccati; Chapter 4. Arithmetic differential geometry: the case of _{ }; 4.1. Arithmetic logarithmic derivative and Ehresmann connections;

505 8 a| 4.2. Existence of Chern connections4.3. Existence of Levi-Cività connections; 4.4. Existence/non-existence of Fedosov connections; 4.5. Existence/non-existence of Lax-type connections; 4.6. Existence of special linear connections; 4.7. Existence of Euler connections; 4.8. Curvature formalism and gauge action on _{ }; 4.9. Non-existence of classical -cocycles on _{ }; 4.10. Non-existence of -subgroups of simple groups; 4.11. Non-existence of invariant adelic connections on _{ }; Chapter 5. Curvature and Galois groups of Ehresmann connections;

505 8 a| 5.1. Gauge and curvature formulas5.2. Existence, uniqueness, and rationality of solutions; 5.3. Galois groups: generalities; 5.4. Galois groups: the generic case; Chapter 6. Curvature of Chern connections; 6.1. Analytic continuation along tori; 6.2. Non-vanishing/vanishing of curvature via analytic continuation; 6.3. Convergence estimates; 6.4. The cases =1 and =1; 6.5. Non-vanishing/vanishing of curvature via correspondences; Chapter 7. Curvature of Levi-Cività connections; 7.1. The case =1: non-vanishing of curvature mod ; 7.2. Analytic continuation along the identity;

520 a| The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to me.;

650 4 a| Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Local ground fields.;

650 7 a| Geometry, Differential.2| fast0| (OCoLC)fst00940919;

650 7 a| Number theory -- Forms and linear algebraic groups -- Classical groups.2| msc;

650 7 a| Number theory -- Discontinuous groups and automorphic forms -- $p$-adic theory, local fields.2| msc;

650 7 a| Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Local ground fields.2| msc;

650 7 a| Differential geometry -- Global differential geometry -- Methods of Riemannian geometry, including PDE methods; curvature restrictions.2| msc;

650 0 a| Geometry, Differential.=| ^A42979;

650 7 a| MATHEMATICS / Geometry / General.2| bisacsh;

655 4 a| Electronic books.;

710 2 a| American Mathematical Societye| issuing body,e| publisher.=| ^A16427;

776 08 i| Print version:z| 9781470436230z| 147043623Xw| (DLC) 2016056302w| (OCoLC)965754191;

830 0 a| Mathematical surveys and monographsv| no. 222.=| ^A638333;

856 40 3| EBSCOhostu| http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1571706;

938 a| EBL - Ebook Libraryb| EBLBn| EBL4940248;

938 a| YBP Library Servicesb| YANKn| 14744571;

938 a| EBSCOhostb| EBSCn| 1571706;

949 a| Click on web addressw| asish| joyner96o| jwjh;

949 a| Click on web addressw| asish| hsl102o| jwjh;

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998 a| 4783241;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 4783241-5001l| HSLELECm| HSLr| Ys| Yt| HGENEBKu| 11/2/2017x| EBOOKz| HERESOURCEo| .STAFF. jwjh;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 4783241-1001l| JNETm| JOYNERr| Ys| Yt| JNE3BKu| 11/2/2017x| EBOOKz| JERESOURCE;

Foundations of arithmetic differential geometry / Alexandru Buium.

Author/creator	Buium, Alexandru, 1955- author.
Other author	American Mathematical Society issuing body, publisher.
Format	Electronic
Publication	Providence, Rhode Island : American Mathematical Society, [2017]
Description	1 online resource.
Supplemental Content	EBSCOhost
Subjects	Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Local ground fields. Geometry, Differential.

Series	Mathematical surveys and monographs ; volume 222 Mathematical surveys and monographs no. 222. ^A638333
Contents	Cover; Title page; Contents; Preface; Acknowledgments; Introduction; 0.1. Outline of the theory; 0.2. Comparison with other theories; Chapter 1. Algebraic background; 1.1. Algebra; 1.2. Algebraic geometry; 1.3. Superalgebra; Chapter 2. Classical differential geometry revisited; 2.1. Connections in principal bundles and curvature; 2.2. Lie algebra and classical groups; 2.3. Involutions and symmetric spaces; 2.4. Logarithmic derivative and differential Galois groups; 2.5. Chern connections: the symmetric/anti-symmetric case; 2.6. Chern connections: the hermitian case
Contents	2.7. Levi-Cività connection and Fedosov connection; 2.8. Locally symmetric connections; 2.9. Ehresmann connections attached to inner involutions; 2.10. Connections in vector bundles; 2.11. Lax connections; 2.12. Hamiltonian connections; 2.13. Cartan connection; 2.14. Weierstrass and Riccati connections; 2.15. Differential groups: Cassidy and Painlevé; Chapter 3. Arithmetic differential geometry: generalities; 3.1. Global connections and their curvature; 3.2. Adelic connections; 3.3. Semiglobal connections and their curvature; Galois connections
Contents	3.4. Curvature via analytic continuation between primes; 3.5. Curvature via algebraization by correspondences; 3.6. Arithmetic jet spaces and the Cartan connection; 3.7. Arithmetic Lie algebras and arithmetic logarithmic derivative; 3.8. Compatibility with translations and involutions; 3.9. Arithmetic Lie brackets and exponential; 3.10. Hamiltonian formalism and Painlevé; 3.11. -adic connections on curves: Weierstrass and Riccati; Chapter 4. Arithmetic differential geometry: the case of _{ }; 4.1. Arithmetic logarithmic derivative and Ehresmann connections
Contents	4.2. Existence of Chern connections4.3. Existence of Levi-Cività connections; 4.4. Existence/non-existence of Fedosov connections; 4.5. Existence/non-existence of Lax-type connections; 4.6. Existence of special linear connections; 4.7. Existence of Euler connections; 4.8. Curvature formalism and gauge action on _{ }; 4.9. Non-existence of classical -cocycles on _{ }; 4.10. Non-existence of -subgroups of simple groups; 4.11. Non-existence of invariant adelic connections on _{ }; Chapter 5. Curvature and Galois groups of Ehresmann connections
Contents	5.1. Gauge and curvature formulas5.2. Existence, uniqueness, and rationality of solutions; 5.3. Galois groups: generalities; 5.4. Galois groups: the generic case; Chapter 6. Curvature of Chern connections; 6.1. Analytic continuation along tori; 6.2. Non-vanishing/vanishing of curvature via analytic continuation; 6.3. Convergence estimates; 6.4. The cases =1 and =1; 6.5. Non-vanishing/vanishing of curvature via correspondences; Chapter 7. Curvature of Levi-Cività connections; 7.1. The case =1: non-vanishing of curvature mod ; 7.2. Analytic continuation along the identity
Abstract	The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to me.
Issued in other form	Print version: 9781470436230 147043623X
Genre/form	Electronic books.
ISBN	9781470440893 (electronic bk.)
ISBN	147044089X (electronic bk.)

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