Homological Algebra: Basics and Applications

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Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Derived Functor Approach

Covers the derived functor approach to Čech cohomology, emphasizing the relationship between derived functors and sheaf theory.

Finite Abelian Groups: Classification Theorem

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Cohomology: Recollection and Foliations

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Coherent Sheaves: Locally Ringed Space

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

Algebraic Cycles and Etale Cohomology

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

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Cohomology of Quasi-Coherent on Affine Schemes

Covers the cohomology of quasi-coherent sheaves on affine schemes.