Foundations of arithmetic differential geometry / Alexandru Buium

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Mathematical surveys and monographs ; volume 222Publisher: Providence, Rhode Island : American Mathematical Society, 2017Description: 1 Online-RessourceSubject(s): Additional physical formats: 147043623X | 9781470436230 | 147044089X. | 9781470440893. | Erscheint auch als: No title Druck-Ausgabe | Print version: No title DDC classification:
  • 516.36
MSC: MSC: *11-02 | 11E57 | 11E08 | 11E95 | 11F85 | 14G20 | 53C05 | 53C21LOC classification:
  • QA641
Online resources: Summary: 3.4. Curvature via analytic continuation between primes3.5. 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 connectionsSummary: 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 identitySummary: 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 mePPN: PPN: 1003051588Package identifier: Produktsigel: ZDB-4-NLEBK
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