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FIELD THEORY (M2, Serre, local)

Lecture Topic : (Pure Math) FIELD THEORY (M2, Serre, local)

Prerequisites : Abstract Algebra (M1); Homology-Cohomology (M1);

Recommended Text(s) :

“Local Fields”, Graduate Texts in Mathematics (GTM) No. 67, Jean-Pierre Serre, Springer, 1980?.

Approx price new on Amazon.com (hard copy) :  $54

Approx price second hand on Amazon.com (hard copy) : $30

Availability free on eMule.com (e-format) : yes?

eMule search key word(s) : Serre, Local Fields

Lectures and Links :

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Lecture 1  (link)

Ch.1   Discrete Valuation Rings and Dedekind Domains

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Lecture 2  (link)

Ch.2   Completion

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Lecture 3  (link)

Ch.3   Discriminant and Different

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Lecture 4 (link)

Ch.4   Ramification Groups

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Lecture 5  (link)

Ch.5   The Norm

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Lecture 6  (link)

Ch.6   Artin Representation

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Lecture 7  (link)

Ch.7   Basic Facts

Appendix : Non-Abelian Cohomology

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Lecture 8  (link)

Ch.8   Cohomology of Finite Groups

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Lecture 9  (link)

Ch.9   Theorems of Tate and Nakayama

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Lecture 10  (link)

Ch.10   Galois Homology

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Lecture 11  (link)

Ch.11   Class Formations

Appendix : Computations of Cup Products

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Lecture 12  (link)

Ch.12   Brauer Group of a Local Field

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Lecture 13  (link)

Ch.13   Local Class Field Theory

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Lecture 14  (link)

Ch.14   Local Symbols and Existence Theorem

Appendix : The Global Case (Statement of Results)

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Lecture 15  (link)

Ch.15  Ramification

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