Geodesic
A generalization of Beilinson's geometric height pairing
Documenta mathematica, Tome 27 (2022), pp. 1671-1692.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In the first section of his seminal paper on height pairings, Beilinson constructed an $\ell$-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 $B$ over an algebraically closed field, with values in the second $\ell$-adic cohomology group of $B$. Over $\mathbf{C}$ our pairing is in fact $\mathbf{Q}$-valued, and in general we speculate about its geometric origin.
Classification : 14C25, 11G50, 14F20
Keywords: algebraic cycle, perverse sheaf, height pairing 
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Rössler, Damian; Szamuely, Tamás. A generalization of Beilinson's geometric height pairing. Documenta mathematica, Tome 27 (2022), pp. 1671-1692. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a24/