Genus one curves over the rationals
Mirela Ciperiani

Let C be a genus one curve defined over Q. Assume that C has a point defined over each completion of Q. The local to global principle suggests that C should have a point defined over Q. In general, this is not the case. The motivating question is: What can be said about such curves C? A first approach is to analyze the fields of definition of the points of C. In joint work with A. Wiles we have shown that C has a point defined over some solvable extension of Q. Another approach is to see how many such curves C there are with a fixed Jacobian. By viewing these curves as cohomology classes we will describe the current understanding of the answer to this question from the point of view of Iwasawa theory.

Colloquium, Department of Mathematics, Rice University
October 9, 2008 HB 227 4-5 PM

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