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Last updated:
November 7, 2022
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
This course is the continuation of 18.785 Number Theory I.
It begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more hands-on introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.
Course Curriculum
- Introduction Unlimited
- Hilbert Symbols Unlimited
- Norm Groups with Tame Ramification Unlimited
- GCFT and Quadratic Reciprocity Unlimited
- Non-Degeneracy of the Adèle Pairing and Exact Sequences Unlimited
- Exact Sequences and Tate Cohomology Unlimited
- Chain Complexes and Herbrand Quotients Unlimited
- Tate Cohomology and Inverse Limits Unlimited
- Hilbert’s Theorem 90 and Cochain Complexes Unlimited
- Homotopy, Quasi-Isomorphism, and Coinvariants Unlimited
- The Mapping Complex and Projective Resolutions Unlimited
- Derived Functors and Explicit Projective Resolutions Unlimited
- Homotopy Coinvariants, Abelianization, and Tate Cohomology Unlimited
- Tate Cohomology and K{{}} Unlimited
- The Vanishing Theorem Implies Cohomological LCFT Unlimited
- Vanishing of Tate Cohomology Groups Unlimited
- Proof of the Vanishing Theorem Unlimited
- Norm Groups, Kummer Theory, and Profinite Cohomology Unlimited
- Brauer Groups Unlimited
- Proof of the First Inequality Unlimited
- Artin and Brauer Reciprocity, Part I Unlimited
- Artin and Brauer Reciprocity, Part II Unlimited
- Proof of the Second Inequality Unlimited
About the instructor
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Massachusetts Institute of Technology
