Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Wednesday, 5 March 2003, 16:00 - 17:00, room 403

Wednesday, 12 March 2003, 16:00 - 17:00, room 403

Theo van den Bogaart: Mochizuki's Hodge-Arakelov theory of elliptic curves

Abstract: The aim of this talk is twofold. The first goal is to discuss part of S. Mochizuki's work towards the construction of an 'arithmetic Kodaira-Spencer morphism'. We will explain the way he constructs such type of maps out of certain cohomological comparison isomorphisms and we discuss how this eventually may lead to a proof of the famous abc-conjecture. A big step in this direction is made by his Hodge-Arakelov comparison isomorphism. The second (much more modest) aim is then to explain some results (which are the subject of my master thesis) about 'polynomial functions on the universal extension of an abelian variety'. This last concept plays an important role in the formulation of Mochizuki's isomorphism.