Algebraic description of complex conjugation on cohomology of a smooth projective hypersurface

Autor:	Park, Jeehoon, Park, Junyeong, Yoo, Philsang
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry 14C30
Druh dokumentu:	Working Paper
Popis:	We describe complex conjugation on the primitive middle-dimensional algebraic de Rham cohomology of a smooth projective hypersurface defined over a number field that admits a real embedding. We use Griffiths' description of the cohomology in terms of a Jacobian ring. The resulting description is algebraic up to transcendental factors explicitly given by certain periods. Comment: The statement and proof of Theorem 2.3 is not correct. What was described in the paper is an order 2 operation which swaps the Hodge components, which gives the complex conjugation only when the Hodge component has dimensions 1. But our description does not give the complex conjugation in the general case where the Hodge component has a bigger dimension
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.14546 Zobrazit plný text záznamu View this record from Arxiv