Math 465: Topics in algebra
Algebraic number theory

Caveat lector: These lecture notes are rough and preliminary in form. Please inform me of any errors you might find.

Lecture 1, January 13 Introduction: Hilbert's Tenth Problem
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Lecture 2, January 15 Reducing mod N
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Lecture 3, January 17 Units modulo prime powers
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A good reference for squares modulo prime powers is:
J. P. Serre, A Course in Arithmetic , II.3

Lecture 4, January 22 Quadratic reciprocity
This can be found in any book on number theory.

Lecture 5, January 24 Chevalley-Warning Theorem
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Lecture 6, January 27 Quadratic forms
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Lecture 7, January 29 General lifting theorems
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