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. |

October 9, 2008 HB 227 4-5 PM