Arithmetic Differential Equations by Alexandru Buium

By Alexandru Buium

This monograph includes intriguing unique arithmetic that might encourage new instructions of analysis in algebraic geometry. constructed here's an mathematics analog of the speculation of standard differential equations, the place capabilities are changed by way of integer numbers, the spinoff operator is changed by means of a ""Fermat quotient operator"", and differential equations (viewed as features on jet areas) are changed by way of ""arithmetic differential equations"". the most software of this thought issues the development and research of quotients of algebraic curves by way of correspondences with countless orbits. this kind of quotient reduces to some extent in algebraic geometry. yet some of the above quotients stop to be trivial (and develop into particularly fascinating) if one enlarges algebraic geometry through the use of mathematics differential equations instead of algebraic equations. This booklet, partly, follows a sequence of papers written via the writer. even if, quite a lot of the fabric hasn't ever been released prior to. for many of the booklet, the single must haves are the elemental proof of algebraic geometry and algebraic quantity thought. it truly is appropriate for graduate scholars and researchers attracted to algebraic geometry and quantity thought.

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