arithmetic geometry

alternative arithmetical geometry

1. uncountablemathematicsA developing branch of mathematics in which techniques of algebraic geometry are applied to number theory, in particular being concerned with schemes of finite type over the spectrum of the ring of integers, Spec(ℤ).

   1994, Nancy Childress, John W. Jones (editors), Arithmetic Geometry: Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, American Mathematical Society, back cover, This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993.

   3 more examples

   Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over nonalgebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory.

   2010, Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta, Arithmetic Geometry: Lectures given at the C.I.M.E. Summer School, Springer, page v

   Their^([semistable models']) occurrence in arithmetic geometry is ubiquitous for the study of ℓ-adic or p-adic cohomology, and of Galois representations.

   2013, Matthieu Romagny, “Models of Curves”, in Pierre Dèbes, Michel Emsalem, Matthieu Romagny, A. Muhammed Uludağ, editors, Arithmetic and Geometry Around Galois Theory, Springer, page 149

   Arakelov geometry is one of the branches in arithmetic geometry.

   2014, Atsushi Moriwaki, Arakelov Geometry, American Mathematical Society, page vii

   Synonyms: arithmetic algebraic geometry, arithmetical algebraic geometry