Poincar\'e duality and unimodularity
Algebraic Geometry
2021-07-06 v4 Algebraic Topology
Number Theory
Abstract
It is well known that the cup-product pairing on the complementary integral cohomology groups (modulo torsion) of a compact oriented manifold is unimodular. We prove a similar result for the -adic cohomology groups of smooth algebraic varieties.
Keywords
Cite
@article{arxiv.1112.1429,
title = {Poincar\'e duality and unimodularity},
author = {Yuri G. Zarhin},
journal= {arXiv preprint arXiv:1112.1429},
year = {2021}
}
Comments
This is a corrected version of my paper [10] that was published in 2012; it turns out that [Lemma 2.5, 10] is wrong. Nevertheless the main results of [10] (Theorem 1.2 and Corollary 1.3) remain valid. Here we present their proofs that are slight modifications of arguments from [10]. I am grateful to Thomas Geisser, who pointed out that Lemma 2.5 of [10] is wrong