Geodesic
A generalization of Beilinson's geometric height pairing
Documenta mathematica, Tome 27 (2022), pp. 1671-1692 Cet article a éte moissonné depuis la source EMS Press

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In the first section of his seminal paper on height pairings, Beilinson constructed an l-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 l-adic cohomology group of B. Over C our pairing is in fact Q-valued, and in general we speculate about its geometric origin.
DOI : 10.4171/dm/x15
Classification : 11G50, 14C25, 14F20
Mots-clés : algebraic cycle, perverse sheaf, height pairing 
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     author = {Tam\'as Szamuely and Damian R\"ossler},
     title = {A generalization of {Beilinson's} geometric height pairing},
     journal = {Documenta mathematica},
     pages = {1671--1692},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x15},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x15/}
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Tamás Szamuely; Damian Rössler. A generalization of Beilinson's geometric height pairing. Documenta mathematica, Tome 27 (2022), pp. 1671-1692. doi: 10.4171/dm/x15

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