Height Pairing on Higher Cycles and Mixed Hodge Structures

J. I. Burgos Gil; S. Goswami; G. Pearlstein

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arXiv · 2007.06036

Height Pairing on Higher Cycles and Mixed Hodge Structures

J. I. Burgos Gil·S. Goswami·G. Pearlstein

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Abstract

For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized complex and intersect properly. In a special case, this mixed Hodge structure is an oriented biextension, and its height agrees with the higher archimedean height pairing introduced in a previous paper by the first two authors. We also compute a non-trivial example of this height given by Bloch-Wigner dilogarithm function. Finally we study the variation of mixed Hodge structures of Hodge-Tate type, and show that the height extends continuously to degenerate situations.

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BibTeX RIS

J. I. Burgos Gil, S. Goswami, G. Pearlstein. 2020-07-12. Height Pairing on Higher Cycles and Mixed Hodge Structures. https://arxiv.org/abs/2007.06036

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