Algebraic Geometry

His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics.

the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories

the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety

the Bombieri-Lang conjecture is an unsolved problem conjectured by Enrico Bombieri and Serge Lang about the Zariski density of the set of rational points of an algebraic variety of general type

the Nakai conjecture is an unproven characterization of smooth algebraic varieties

the Nagata conjecture on curves, named after Masayoshi Nagata, governs the minimal degree required for a plane algebraic curve to pass through a collection of very general points with prescribed multiplicities

In arithmetic geometry, the uniform boundedness conjecture for rational points asserts

Ott-Heinrich Keller was a German mathematician who worked on algebraic geometry and topology.

With Yosikazu Nakai, he published Algebraic geometry

His work in algebraic geometry uses the ideal theory in polynomial rings

In mathematics, especially algebraic geometry, the Bass conjecture says that certain algebraic K-groups are supposed to be finitel

In mathematics, more specifically in algebraic geometry, Parshin's conjecture (also referred to as the Beilinson-Parshin conjectur

In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent

In algebraic geometry, Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces o

In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of

mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromor

algebraic geometry

algebraic geometers

Gerd Faltings (German: [ɡɛʁt ˈfaltɪŋs] ; born 28 July 1954) is a German mathematician known for his work in arithmetic geometry.

He was well known for his work in algebraic geometry. == Biography == Chow was a student in the US, graduating from the University of Chicago in 1931.

He died on August 28, 1961, in Rosario, Argentina, and was buried in the Jewish cemetery there. == Mathematical contributions == His early work studied singularities on algebraic curves and surfaces.

Nicholas Ian Shepherd-Barron, FRS (born 17 March 1955), is a British mathematician working in algebraic geometry.

Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in material object, and in numerous applications in the physical sciences.

This construction is a global version of the construction of the divisor class group, or ideal class group, and is much used in algebraic geometry and the theory of complex manifolds.

They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory.

The proof uses many techniques from algebraic geometry and number theory and has many ramifications in these branches of mathematics.

whose work was mainly on projective and algebraic geometry

Algebra Algebraic Geometry

Algebra Algebraic Geometry

Algebra Algebraic Geometry

in invariant theory, and are at the basis of modern algebraic geometry. The two other theorems are Hilbert's basis theorem

In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection

where V is a non-singular n-dimensional projective algebraic variety over the field Fq with q elements and Nk is the

In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0

Hasse's theorem on elliptic curves, also referred to as the Hasse bound, provides

shows that a specific collection of k double points in the projective space Pr will impose independent types of conditions

Jean-Pierre Serre is a French mathematician who has made important contributions to algebraic topology, algebraic geometry, and algebraic number theory.

Enrico Bombieri is an Italian Fields medal winner, known for his work in analytic number theory, algebraic geometry, theory of several complex variables, minimal surfaces and the theory of finite groups.

Lang's mathematical research ranged over a wide range of topics such as algebraic geometry, Diophantine geometry

Émile Picard worked in algebraic geometry as well as elasticity, heat and electricity.

Alfred Clebsch was a German mathematician worked on algebraic geometry and was a co-founder of Mathematische Annalen .