Counterexample to the Hodge Conjecture

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We construct a K3 surface whose transcendental lattice has a self-isomorphism which is not a linear combination of self-isomorphisms over $\mathbb{Q}$ which preserve cup products up to nonzero multiples. Products of it with itself give candidates for counterexamples to the Hodge conjecture which may be of interest. We also study the Kuga-Satake construction in relation to these examples.
We no longer claim to have disproved the Hodge conjecture. Section 5 is deleted except for 5.3, and Theorems 6.2,6.3 are deleted

Keywords

Algebraic Geometry, 14C30

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/115370

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608265
 http://arxiv.org/abs/math/0608265

Collections

arXiv