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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.

Assessment

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.

Certification

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Course Credit: MIT

Course Curriculum

Module: 01
Introduction 00:30:00
Hilbert Symbols 00:30:00
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
Module: 02
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
Module: 03
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
Module: 04
Brauer Groups 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
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

Course Reviews

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