Here is a list of articles in the category Localization (mathematics) of the Computing portal that unifies foundations of mathematics and computations using computers. In mathematics, specifically algebraic geometry and its applications, localization is a way of studying an algebraic object "at" a prime. One may study an object by studying it at every prime (the "local question"), then piecing these together to understand the original object (the "local-to-global question"). The simplest example is solving a Diophantine equation (a polynomial with integer coefficients) by finding solutions mod every prime (properly, finding a p-adic solution for every prime p), then piecing these solutions together, which is called the Hasse principle.
from the point of view of the spectrum of a ring, the primes are the points of a ring, and thus localization studies a ring (or similar algebraic object) at every point, then the local-to-global question asks to piece these together to understand the entire space.
Pages in category "Localization (mathematics)"
The following 12 pages are in this category, out of 12 total.
- Discrete valuation ring (computing)
- Hasse principle (computing)
- Semi-local ring (computing)
- Valuation ring (computing)