Instructional Workshop on Class Field Theory
January 22-26, 2018 KIAS 1423 |
Prerequisite | Home > Prerequisite |
We try to minimize the prerequisite, but it seems difficult to minimize more than the below.
● 1st year graduate algebra (A reasonable amount of Dummit-Foote should be fine.)
● one semester course on algebraic number theory (Chapter 1 of Neukirch's 'Algebraic Number Theory' is fine.)
● the familiarity with p-adic numbers (The first half of Chapter 2 of Neukirch's 'Algebraic Number Theory' is fine.)
● more than one semester course on complex analysis
More explicitly, we expect the attendees are comfortable with most of the following words:
number fields and their rings of integers, unit groups of the rings of integers, norm of ideals, discriminants of number fields, Dedekind domains and unique prime factorization, fractional ideals, class numbers and their finiteness, Dirichlet unit theorem, the behavior of prime ideals in field extensions: split, inert, and ramified, decomposition groups, inertia groups, Frobenius map, cyclotomic fields, localization of rings, discrete valuation rings and valuations, completion of rings with respect to ideals, p-adic numbers, local fields, the multiplicative structure of local fields, p-adic logarithm and exponential.
"Comfortable" does NOT mean you understand every single detail. Do not worry about a little missing gaps too much.