Number Theory Seminar

Wednesday 4/9/03 3:30-4:30 PM in Hylan 1104, and
Wednesday 4/16/03 3:30-4:30 PM in Hylan 1104:
Doug Ravenel- "Formal group laws associated with algebraic curves"

ABSTRACT:

Associated to each algebraic curve X is the group of divisor classes called its Jacobian J(X). If X is a defined over the complex numbers and has genus g, then J(x) is a 2g-dimensional torus. If X is an elliptic curve, the J(X) is X itself. In any case we can look at this group near its identity element and write down its multiplication map as power series in local coordinates; this is called a formal group law for X. In the first talk I will describe the general theory of such formal group laws, and in the second talk I will show how to compute it explicitly for certain curves.