2020/09/02 by Damian Rössler, Rössler, Damian, Tamás Szamuely +1 · 2 citations
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Alkaloids: synthesis and pharmacology
paper · pdf · doi:10.48550/arxiv.2009.01191
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 projective varieties over the function field of a curve over an algebraically closed field, and asked about an 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 \Bbb C our pairing is in fact \Bbb Q-valued, and in general we speculate about its geometric origin.