Higher Arithmetic Intersection Theory

We give a new definition of higher arithmetic Chow groups for smooth projective varieties defined over a number field, which is similar to Gillet and Soul\'e's definition of arithmetic Chow groups. We also give a compact description of the intersection theory of such groups. A consequence...

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Bibliographic Details
Main Authors Burgos-Gil, José Ignacio, Goswami, Souvik
Format Journal Article
LanguageEnglish
Published 29.12.2017
Subjects
Mathematics - Algebraic Geometry
Mathematics - K-Theory and Homology
Mathematics - Number Theory
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Summary:We give a new definition of higher arithmetic Chow groups for smooth projective varieties defined over a number field, which is similar to Gillet and Soul\'e's definition of arithmetic Chow groups. We also give a compact description of the intersection theory of such groups. A consequence of this theory is the definition of a height pairing between two higher algebraic cycles, of complementary dimensions, whose real regulator class is zero. This description agrees with Beilinson's height pairing for the classical arithmetic Chow groups. We also give examples of the higher arithmetic intersection pairing in dimension zero that, assuming a conjecture by Milnor on the independence of the values of the dilogarithm, are non zero.
DOI:10.48550/arxiv.1712.10150