Ringed Spaces: Definitions and Properties

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Related lectures (32)

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Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Sheaves and Modules

Covers sheaves and modules, including morphisms, sheafification, cocalization, and direct image properties.

Sheaves: Hartshorne I.1

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Redly Constructed Morphisms

Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.

Group Morphisms: G-equivariant, Chapter III

Discusses the formulation of G-morphisms within vector spaces and topological spaces.

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

Sheafification: Natural Procedure and Adjoints

Covers sheafification, adjoint functors, and challenges in ensuring sheaf properties.

Regular Functions on Quasi-Affine Varieties

Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.