|Lectures||MWF 10:10–11:00, online|
|Prerequisites||Math 254A and 256A|
|Catalog Description||Math 254AB: Valuations, units, and ideals in number fields, ramification theory, quadratic and cyclotomic fields, topics from class field theory, zeta-functions and L-series, distribution of primes, modular forms, quadratic forms, diophantine equations, p-adic analysis, and transcendental numbers.|
|Syllabus||I plan to cover the more advanced topic of Arakelov theory, including applications to diophantine problems.|
|Grading||Grades will be based on homework assignments, and possibly in-class quizzes. There will be no final exam, but the last problem set will be due sometime during the week of final exams.|
|Homework||Weekly or biweekly, assigned in class|
|1||January 22||Solution to Hartshorne II Ex. 3.15||download|
|2||January 29||Nonsingular projective curves and their function fields||dvi|
|3||February 6||Chapter 0: Preliminary material (for reference only) (revised 2/13)||dvi|
|4||February 13||Chapter 1: Heights||dvi|
|5||March 1||Chapter 2: Weil functions||dvi|
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Last updated 1 March 2021