Arithmetic and motivic aspects of the Kuga-Satake construction

Samenvatting

The central theme of the project is the Kuga-Satake construction. The first main goal is to prove the Tate conjecture for surfaces of geometric genus 1 in characteristic 0. This would provide a new class of varieties where, using advanced techniques, we can obtain positive results on one of the fundamental open problems in algebraic geometry. Our approach is based on a refinement of a method of Deligne and Andre.

A second main topic is the question whether the Kuga-Satake correspondence is given by an algebraic cycle, as predicted by the Hodge conjecture. This is a fundamental open problem. Related to this is the question whether we can define a Kuga-Satake construction over an arithmetic base; this leads us to study the morphism of moduli spaces given by the Kuga-Satake construction. Our goal is to prove that this morphism is defined over a number field and that it extends to mixed characteristics.

Producten

Wetenschappelijk artikel

Proefschrift

  • J Commelin(2017): On l-adic compatibility for abelian motives & the Mumford-Tate conjecture for products of K3 surfaces , ??  7 juli 2017

Kenmerken

Projectnummer

613.001.207

Hoofdaanvrager

Prof. dr. B.J.J. Moonen

Verbonden aan

Radboud Universiteit Nijmegen, Faculteit der Natuurwetenschappen, Wiskunde en Informatica, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP)

Uitvoerders

J.M. Commelin BSc

Looptijd

01/09/2013 tot 01/09/2017