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 Kingdom
  • Tamás Szamuely

    Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
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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.

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Damian Rössler, Tamás Szamuely, A generalization of Beilinson's geometric height pairing. Doc. Math. 27 (2022), pp. 1671–1692

DOI 10.4171/DM/X15