|Universiteit Faculteit FNWI English version||1 maart 2005, e-mail|
Woensdag 16 maart 2005
AbstractAn elliptic curve E is the solution set of an equation y2=x3+Ax+B, for some constants A,B, together with a point O `at infinity'. This point O is needed to obtain a compact curve. If one chooses A and B in some number field one can study the arithmetic of the elliptic curve. This theory is quite far developed.
Our talk will focus on elliptic surfaces, i.e., one dimensional families of elliptic curves. In our talk this means that the above mentioned A and B are replaced by rational functions A(t), B(t). If A(t) and B(t) have coefficients in a number field, then we can study the arithmetic of the elliptic surface. This theory is not very far developed yet.
In this talk we introduce several important arithmetic invariants of elliptic surfaces and we discuss how one can calculate them.