Concept

Derived algebraic geometry

Related lectures (31)

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Cartier Divisors and Invertible Sheaves

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

Quotient Criterion

Explores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant morphisms.

Algebraic Geometry: Forms and Maps

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Motivic Knot Theory: Quadratic Linking Degree

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, oriented links, intersection theory, and examples like the Hopf and Solomon links.

Affine Varieties and Hypersurfaces

Explores affine varieties, hypersurfaces, dimension in algebraic geometry, minimal prime ideals, and local properties of plane curves.

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.

Modern Algebraic Geometry: Schemes and Affine Schemes

Covers modern algebraic geometry, focusing on schemes and affine schemes, including a review of classical algebraic geometry and Bézout's theorem.

Geometric Objects in Algebra

Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Tangent Spaces Insights

Explores the relationships between tangent spaces, dimensions, and sub-varieties in algebraic geometry.

Tangent Spaces in Algebraic Geometry

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

Adjunctions and Applications

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

Position Space Approach: Analyzing Banana Feynman Diagrams

Presents the position space approach to banana Feynman diagrams and their differential equations.

Primary Decomposition: Behaviour and Localisation

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

The Quadratic Linking Degree

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Locally Noetherian Schemes

Covers the concept of locally Noetherian schemes in algebraic geometry.

Differential of a Morphism

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.