After studying Theory of Numbers, Class Field Theory deals with abelian extensions of local fields and global fields with various arithmetic properties of the abelian extensions. To prove Artin-Verdier Duality, many subareas of algebraic number theory, Class-Field-Theory is used where this [course_title] will help you understand effectively. This [course_title] will provide you with Quadratic extensions and Hilbert symbols, Homological algebra, Galois Cohomology etc. in details to meet your needs.
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
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Course Credit: MIT
|Norm Groups with Tame Ramification||00:30:00|
|GCFT and Quadratic Reciprocity||00:30:00|
|Non-Degeneracy of the Adèle Pairing and Exact Sequences||00:30:00|
|Exact Sequences and Tate Cohomology||00:30:00|
|Chain Complexes and Herbrand Quotients||00:30:00|
|Tate Cohomology and Inverse Limits||00:30:00|
|Hilbert’s Theorem 90 and Cochain Complexes||00:15:00|
|Homotopy, Quasi-Isomorphism, and Coinvariants||00:30:00|
|The Mapping Complex and Projective Resolutions||00:30:00|
|Derived Functors and Explicit Projective Resolutions||00:30:00|
|Homotopy Coinvariants, Abelianization, and Tate Cohomology||00:30:00|
|Tate Cohomology and Kunr||00:30:00|
|The Vanishing Theorem Implies Cohomological LCFT||00:30:00|
|Vanishing of Tate Cohomology Groups||00:30:00|
|Proof of the Vanishing Theorem||00:30:00|
|Norm Groups, Kummer Theory, and Profinite Cohomology||00:30:00|
|Proof of the First Inequality||00:30:00|
|Artin and Brauer Reciprocity – Part I||00:15:00|
|Artin and Brauer Reciprocity – Part II||00:30:00|
|Proof of the Second Inequality||00:30:00|
|Submit Your Assignment||00:00:00|
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