Concept

Ringed space

Related lectures (15)

Ringed Spaces: Definitions and Properties

Covers the definitions and properties of ringed spaces, including morphisms and examples of locally ringed spaces.

Explores derivations and the Zariski tangent space in algebraic geometry, emphasizing their importance and practical applications.

Abélianization: Fundamental Groups

Explores abélianization of fundamental groups in commutative spaces with examples and proofs.

Vector Bundles & Locally Free Sheaves

Covers vector bundles, locally free sheaves, depth, Serre twisting sheaf, and graded modules in algebraic geometry.

Algebraic Geometry: Localization and Prime Ideals

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

Coherent Sheaves: Locally Ringed Space

Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.

Primary Decomposition: Behaviour and Localisation

Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Ring Structure: Polynomials and Coefficients

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Adjunctions and Applications

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Ideals in Commutative Rings

Covers the concept of ideals in commutative rings and their role in ring homomorphisms.

Sheaf Morphisms and Localization

Explores F-G sheaf morphisms, sheafification, and localization in ring theory.

Discrete Valuation Rings

Explores discrete valuation rings, their properties, uniqueness of representation, and relationship with principal ideal domains.

Congruence Relations in Rings

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.