Burgos Gil, Jose Ignacio and Goswami, Souvik and Pearlstein, Gregory (2022) Height pairing on higher cycles and mixed Hodge structures. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 125 (1). pp. 61-170. ISSN 0024-6115, 1460-244X
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DEGENERATIONS; FORMS |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 10:17 |
| Last Modified: | 07 Feb 2024 10:17 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57189 |
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