Algebraic Geometry: Regularity and Divisors

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Locally Noetherian Schemes

Covers the concept of locally Noetherian schemes in algebraic geometry.

Regularity of Curves

Explores the regularity of curves over a field and the importance of specific properties for curve regularity.

Finite Abelian Groups & Rings

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Integral Domains and Abelian Groups

Discusses integral domains, abelian groups, invertibility, zero divisors, prime elements, and group classification.

Cartier Divisors and Invertible Sheaves

Covers Cartier divisors, invertible sheaves, and their properties in algebraic geometry.

Integers: Well Ordering and Induction

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

Projective Morphisms: Theory and Applications

Explores projective morphisms, graded modules, and their applications in algebraic geometry, emphasizing their properties and construction.

Coherent Sheaves: Locally Ringed Space

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

Regularity and Integrality

Covers regularity and integrality in local Noether rings and affine rings.

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.