BRANCH OF MATHEMATICS DEALING WITH ALGEBRAIC VARIETIES AND THEIR GENERALIZATIONS (SCHEMES, ETC.)
Algebraic Geometry; Computational algebraic geometry; History of algebraic geometry; Applications of algebraic geometry
Algebraicgeometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraicgeometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.
BRANCH OF MATHEMATICS GENERALIZING ALGEBRAIC GEOMETRY SO THAT COMMUTATIVE RINGS PROVIDING LOCAL CHARTS ARE REPLACED BY SIMPLICIAL COMMUTATIVE RINGS OR E∞-RING SPECTRA, WHOSE HIGHER HOMOTOPY GROUPS ACCOUNT FOR NON-DISCRETENESS OF THE STRUCTURE SHEAF
Derived algebraicgeometry is a branch of mathematics that generalizes algebraicgeometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over \mathbb{Q}), simplicial commutative rings or E_{\infty}-ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g.
In mathematics, arithmetic geometry is roughly the application of techniques from algebraicgeometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.
1. US mathematician David Mumford, a professor at Brown University’s Applied Mathematics Division, was co–winner of the Wolf Prize on Sunday for his groundbreaking theoretical work in algebraic geometry.