- Abstract algebra
- >
- Fields of abstract algebra
- >
- Algebraic geometry
- >
- Topological methods of algebraic geometry

- Abstract algebra
- >
- Fields of abstract algebra
- >
- Algebraic topology
- >
- Topological methods of algebraic geometry

- Algebraic topology
- >
- Homological algebra
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

- Category theory
- >
- Homological algebra
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

- Fields of abstract algebra
- >
- Category theory
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

- Fields of abstract algebra
- >
- Homological algebra
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

- Fields of mathematics
- >
- Fields of abstract algebra
- >
- Algebraic geometry
- >
- Topological methods of algebraic geometry

- Fields of mathematics
- >
- Fields of abstract algebra
- >
- Algebraic topology
- >
- Topological methods of algebraic geometry

- Fields of mathematics
- >
- Topology
- >
- Algebraic topology
- >
- Topological methods of algebraic geometry

- Fields of mathematics
- >
- Topology
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

- Functions and mappings
- >
- Category theory
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

- Geometry
- >
- Fields of geometry
- >
- Algebraic geometry
- >
- Topological methods of algebraic geometry

- Geometry
- >
- Topology
- >
- Algebraic topology
- >
- Topological methods of algebraic geometry

- Geometry
- >
- Topology
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

- Mathematical structures
- >
- Category theory
- >
- Sheaf theory
- >
- Topological methods of algebraic geometry

Coherent duality

In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of com

Coherent sheaf

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. The de

Essentially finite vector bundle

In mathematics, an essentially finite vector bundle is a particular type of vector bundle defined by Madhav V. Nori, as the main tool in the construction of the fundamental group scheme. Even if the d

Sheaf cohomology

In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology describes the obstructio

Genus of a multiplicative sequence

In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to sui

Coherent sheaf cohomology

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties. Many geometric questio

Nori-semistable

In mathematics, a Nori semistable vector bundle is a particular type of vector bundle whose first definition has been first implicitely suggested by Madhav V. Nori, as one of the main ingredients for

Homotopical algebra

In mathematics, homotopical algebra is a collection of concepts comprising the nonabelian aspects of homological algebra as well as possibly the abelian aspects as special cases. The homotopical nomen

Chow group

In algebraic geometry, the Chow groups (named after Wei-Liang Chow by Claude Chevalley) of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological space. The

Hirzebruch–Riemann–Roch theorem

In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch's 1954 result generalizing the classical Riemann–Roch theorem on

Fundamental group scheme

In mathematics, the fundamental group scheme is a group scheme canonically attached to a scheme over a Dedekind scheme (e.g. the spectrum of a field or the spectrum of a discrete valuation ring). It i

Multiplicative sequence

In mathematics, a multiplicative sequence or m-sequence is a sequence of polynomials associated with a formal group structure. They have application in the cobordism ring in algebraic topology.

Weil conjectures

In mathematics, the Weil conjectures were highly influential proposals by André Weil. They led to a successful multi-decade program to prove them, in which many leading researchers developed the frame

Kodaira vanishing theorem

In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indice

Étale fundamental group

The étale or algebraic fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces.

Arithmetic genus

In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface.

Riemann–Roch theorem

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions wit

Sheaf (mathematics)

In mathematics, a sheaf is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For e

Motive (algebraic geometry)

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the vast array of similarly behaved cohomology theorie

Grothendieck–Riemann–Roch theorem

In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem

Motivic cohomology

Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a special case. S

Vanishing cycle

In mathematics, vanishing cycles are studied in singularity theory and other parts of algebraic geometry. They are those homology cycles of a smooth fiber in a family which vanish in the . For example

Weil cohomology theory

In algebraic geometry, a Weil cohomology or Weil cohomology theory is a cohomology satisfying certain axioms concerning the interplay of algebraic cycles and cohomology groups. The name is in honor of

Local cohomology

In algebraic geometry, local cohomology is an algebraic analogue of relative cohomology. Alexander Grothendieck introduced it in seminars in Harvard in 1961 written up by , and in 1961-2 at IHES writt

Cartan's theorems A and B

In mathematics, Cartan's theorems A and B are two results proved by Henri Cartan around 1951, concerning a coherent sheaf F on a Stein manifold X. They are significant both as applied to several compl

Brauer group

In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras

Serre duality

In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The basic version applies to vector bu

Tate conjecture

In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois

Nakano vanishing theorem

In mathematics, specifically in the study of vector bundles over complex Kähler manifolds, the Nakano vanishing theorem, sometimes called the Akizuki–Nakano vanishing theorem, generalizes the Kodaira

Étale cohomology

In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grot

Lefschetz hyperplane theorem

In mathematics, specifically in algebraic geometry and algebraic topology, the Lefschetz hyperplane theorem is a precise statement of certain relations between the shape of an algebraic variety and th

Riemann–Roch theorem for surfaces

In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first given by Castelnuovo , after preliminary ver

© 2023 Useful Links.