Word.ws English Dictionary

arithmetic geometry

arithmetic geometry noun: a 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).

Noun

arithmetic geometry (uncountable)

  1. A 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).
    • This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993.1994, Nancy Childress, John W. Jones (editors), Arithmetic Geometry: Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, American Mathematical Society, back cover
    • 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
    Synonyms:
    arithmetic algebraic geometry, arithmetical algebraic geometry

Examples of arithmetic geometry in a sentence

  • 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...
  • Arakelov geometry is one of the branches in arithmetic geometry.2014, Atsushi Moriwaki, Arakelov Geometry, American Mathematical Society, page vii:

Synonyms of arithmetic geometry

  • arithmetic algebraic geometry
  • arithmetical algebraic geometry

Forms of arithmetic geometry

alternative formarithmetical geometry

Questions about arithmetic geometry

What does arithmetic geometry mean?
Arithmetic geometry means a 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).
How do you use arithmetic geometry in a sentence?
Their^([semistable models']) occurrence in arithmetic geometry is ubiquitous for the study of ℓ-adic or p-adic cohomology, and of Galois representations.
What part of speech is arithmetic geometry?
Arithmetic geometry is a noun.

Words near arithmetic geometry in the dictionary

  1. arithmetic combinatorics
  2. arithmetic densities
  3. arithmetic density
  4. arithmetic function
  5. arithmetic functions
  6. arithmetic geometry
  7. arithmetic hierarchies
  8. arithmetic hierarchy
  9. arithmetic logic unit
  10. arithmetic logic units
  11. arithmetic mean

Source and license

Adapted from Wiktionary: arithmetic geometry (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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