Number Theory Seminar

Wild symbols in local class field theory

Michiel Kosters, Mathematics, University of California, Irvine,

Abstract: Let K be a local field with residue field of characteristic p>0. Our goal is to understand the cyclic extensions of K of degree a power of p. If K has characteristic 0 and contains a p^m-th primitive root of unity, then one can use class field theory and Kummer theory to construct a symbol which helps us to understand the ramification of cyclic extensions of degree p^m. If K has characteristic p, then one can construct a symbol, using class field theory and Artin-Schreier-Witt theory, which helps us to understand the cyclic extensions of degree p^m for any m. We will discuss both symbols in more detail and discuss methods for computing these symbols. The first part is joint work with Jan Bouw and Hendrik Lenstra. The second part is joint work with Chris Davis and Daqing Wan.

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