Lectures related to Smooth morphism

Étale Motives and the Hodge Conjecture

Explores étale motivic cohomology and the Hodge conjecture with a focus on counter-examples.

Varieties with nef anti-canonical: Surjective Albanese

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

Laplace Equation: Decomposition and Solutions

Covers the Laplace equation, decomposition of linear problems, and solutions through separation of variables.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Compact Manifolds Classification

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.

Projective Morphisms: Theory and Applications

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

Regularity and Geometric Meaning

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

Differential Forms on Manifolds

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

Integration Theory: Berkovich Spaces

Explores integration theory over real numbers and Berkovich spaces, revealing intriguing asymmetries and unsolved conjectures.

Approximation in Sobolev Spaces

Covers the approximation of functions in Sobolev spaces using smooth functions.

Ring Theory: Morphisms and Isomorphisms

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Canonical Embedding: Fields and Lattices

Explores canonical embedding of #-fields, lattices, and finiteness of class groups.

Field of Fractions: Definition and Properties

Covers the definition and properties of a field of fractions.

Differential of a Morphism

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

Smooth Projective Varieties

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

Algebraic Structures of Morphism Spaces

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Primary Decomposition: Understanding Schemes

Explores primary decomposition and schemes in algebraic geometry, emphasizing the importance of working over non-algebraically closed fields and the concept of fibers of morphisms.

Injective Morphisms in Mathematics

Introduces injective morphisms and vector spaces with examples and verification methods.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.