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报告人   加藤和也Kazuya Kato, University of Chicago

 Height functions for motives, Hodge analogues, and Nevanlinna analogues

  2017.09.27(星期三),16 :30-17:30

  点:数学院南楼N913

要:

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.

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