By Alexandru Buium
This monograph includes intriguing unique arithmetic that may encourage new instructions of analysis in algebraic geometry. constructed this is an mathematics analog of the idea of normal differential equations, the place features are changed by way of integer numbers, the spinoff operator is changed via a ""Fermat quotient operator"", and differential equations (viewed as services on jet areas) are changed by way of ""arithmetic differential equations"". the most program of this conception matters the development and examine of quotients of algebraic curves by means of correspondences with endless orbits. such a quotient reduces to some degree in algebraic geometry. yet some of the above quotients stop to be trivial (and turn into particularly attention-grabbing) if one enlarges algebraic geometry by utilizing mathematics differential equations as opposed to algebraic equations. This ebook, partially, follows a chain of papers written by way of the writer. even if, quite a lot of the fabric hasn't ever been released ahead of. for many of the ebook, the single necessities are the fundamental proof of algebraic geometry and algebraic quantity concept. it truly is appropriate for graduate scholars and researchers attracted to algebraic geometry and quantity thought.