A generalization of Beilinson's geometric height pairing
Damian Rössler
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United KingdomTamás Szamuely
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Abstract
In the first section of his seminal paper on height pairings, Beilinson constructed an -adic height pairing for rational Chow groups of homologically trivial cycles of complementary codimension on smooth proper varieties over the function field of a curve over an algebraically closed field, and asked about a generalization to higher dimensional bases. In this paper we answer Beilinson's question by constructing a pairing for varieties defined over the function field of a smooth variety over an algebraically closed field, with values in the second -adic cohomology group of . Over our pairing is in fact -valued, and in general we speculate about its geometric origin.
Cite this article
Damian Rössler, Tamás Szamuely, A generalization of Beilinson's geometric height pairing. Doc. Math. 27 (2022), pp. 1671–1692
DOI 10.4171/DM/X15