PrerequisiteComplex analysis in one variableAbstractThis is an undergraduate and first year graduate course on arithmetic of elliptic curves and modular forms with an eye toward generalizations for Calabi-Yau varieties, and in particular Calabi-Yau threefolds. The course will consist of two sub courses. The first one will be dedicated to many well-known topics related to elliptic curves and it ...
AbstractWe consider an elliptic curve E which does not admit complex multiplication, and discuss its arithmetic over the cyclotomic Z_p-extension and more general p-adic Lie extensions of various base fields F. After reviewing some known results over number fields, we shift our focus to the case of global function fields. In this context, we introduce an invariant which is defined without assum...