Advanced Number Theory

1 Course Unit

Ramification theory, adeles and ideles, Tate's thesis, group cohomology and Galois cohomology, class field theory in terms of ideles and cohomology, Lubin-Tate formal groups, Artin and Swan conductors, central simple algebras over local and global fields, general Hasse principles. Other topics may include the following: zero-dimensional Arakelov theory, Tate duality, introduction to arithmetic of elliptic curves, local and global epsilon factors in functional equations, p-adic L- functions and Iwasawa theory, modular forms and functions and modular curves. Not Offered Every Year Prerequisite: MATH 6200 AND MATH 6210 1 Course Unit