High Quality Content by WIKIPEDIA articles! Galois geometry is geometry over a finite field (a "Galois" field), particularly algebraic geometry and analytic geometry; it is a branch of finite geometry. Objects of study include vector spaces (and affine spaces) and projective spaces over finite fields. More narrowly, a Galois geometry may be defined as a projective space over a finite field. Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of polynomial equations in many variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations, as to find some solution; this leads into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.

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