Title: Height functions for motives, Hodge analogues, and Nevanlinna analogues
Speaker: 加藤和也 (Kazuya Kato, University of Chicago)
Time: 2017-9-27, 16:30-17:30
Place: N913
Abstract: We compare height functions for
(1) points of an algebraic variety over a number field,
(2) motives over a number field,
(3) variations of Hodge structure with log degeneration on a projective smooth curve over the complex number field,
(4) horizontal maps from the complex plane C to a toroidal partial compactification of the period domain.
Usual Nevanlinna theory uses height functions for
(5) holomorphic maps f from C to a compactification of an agebraic variety V and considers how often the values of f lie outside V. Vojta compares (1) and (5). In (4), V is replaced by a period domain. The comparisons of (1)--(4) provide many new questions to study.