Math 720, Fall 2013
Advanced Number Theory
- Faculty: David Harbater
harbater AT math.upenn.edu
- Telephone: (215) 898-9594; Department office: (215) 898-8178
- Office: DRL
4E2A; Department office: DRL 4W1-6.
- Office hours: After class, by appointment, and as scheduled.
Advanced Number Theory: This course will focus on local fields and Galois cohomology. It is recommended for graduate students in algebra, including those interested in number theory and in algebraic geometry from an algebraic point of view. The only prerequisite is Math 602; students may or may not have taken Math 620. The course is a prerequisite for Math 721, which will be taught in the spring.
Topics will include local and global fields, Galois theory of local fields, ramification groups, profinite groups, infinite Galois theory, group cohomology, and Galois cohomology.
schedule: Mon and Wed, 1:30-3pm in DRL 4C6.
- Main references:
- Jean-Pierre Serre. Local fields. Graduate Texts in Mathematics, vol. 67, Springer, 1979.
- Jean-Pierre Serre. Galois cohomology. Springer Monographs in Mathematics, 2002.
- Stephen S. Shatz. Profinite groups, arithmetic, and geometry. Annals of Math Studies, number 67, Princeton U. Press, 1972.
- Course structure: The class will meet twice weekly. There will be homework assignments, and students will make oral presentations toward the end of the semester. Topics for these presentations may be chosen from a list of possibilities, or students may choose their own topics related to the material in this course.
Homework assignments for Math 720
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