Lectures related to Étale morphism

Covers morphism of schemes, affine covering, integral homomorphism, and properties of finite maps.

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Manifolds: Charts and Compatibility

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

Ring Theory: Morphisms and Isomorphisms

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

Morphism of Groups

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Groups & Subgroups: Definitions, Theorems, and Morphisms

Covers the fundamental concepts of groups and subgroups, including definitions, theorems, and morphisms.

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.

Algebraic Structures: Modules and Morphisms

Explores modules, sub-modules, and morphisms in algebraic structures.

Hamiltonian Homeomorphisms on Surfaces

Explores the action of Hamiltonian homeomorphisms on surfaces and discusses related mathematical concepts.

Ringed Spaces: Definitions and Properties

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

Ramified Extensions: Eisenstein Polynomials

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Geometric Objects in Algebra

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

Properties of Cartesian Products and Disjoint Unions

Introduces essential properties of Cartesian products and disjoint unions in the theory of groups and categories.

Isomorphism Criterion of Coverings

Covers the isomorphism of coverings and the lifting theory.

Algebraic Cycles and Etale Cohomology

Explores algebraic cycles, etale cohomology, and counterexamples to the Hodge conjecture.

Fixed points, orbits, and stabilizers

Covers fixed points, orbits, and stabilizers in G-varieties, including properties of closed subgroups and faithful actions.

Adjunctions and Applications

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

Simplicial Sets: Introduction and Products

Introduces simplicial sets and explores the construction of products with a geometric interpretation.

Orbital and Fixed Point Functors

Formalizes the construction of orbits and fixed points in group actions, defining morphisms and verifying naturalness.

Understanding Lifting Properties in Homotopy Theory

Focuses on lifting properties in homotopy theory of chain complexes.