{"product_id":"arithmetic-differential-equations-hardback-9780821838624","title":"Arithmetic Differential Equations (Hardback) 9780821838624","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eArithmetic Differential Equations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eAlexandru Buium (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780821838624\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 September 2005\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e310 pages, illustrations\u003cbr\u003e26.2 x 18.6 x 2.4 cm, 0.822 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis monograph contains exciting original mathematics that will inspire new directions of research in algebraic geometry. Developed here is an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a 'Fermat quotient operator', and differential equations (viewed as functions on jet spaces) are replaced by 'arithmetic differential equations'. The main application of this theory concerns the construction and study of quotients of algebraic curves by correspondences with infinite orbits.Any such quotient reduces to a point in algebraic geometry. But many of the above quotients cease to be trivial (and become quite interesting) if one enlarges algebraic geometry by using arithmetic differential equations in place of algebraic equations. This book, in part, follows a series of papers written by the author. However, a substantial amount of the material has never been published before. For most of the book, the only prerequisites are the basic facts of algebraic geometry and algebraic number theory. It is suitable for graduate students and researchers interested in algebraic geometry and number theory.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eMain concepts and results: Preliminaries from algebraic geometry Outline of $\\delta$-geometry General theory: Global theory Local theory Birational theory Applications: Spherical correspondences Flat correspondences Hyperbolic correspondences List of results Bibliography Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003c\/font\u003e","brand":"American Mathematical Society","offers":[{"title":"Brand New","offer_id":52574567891224,"sku":"9780821838624","price":83.69,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/arithmetic-differential-equations-hardback-9780821838624","provider":"Freshly Printed Books","version":"1.0","type":"link"}