Arithmetic and motivic aspects of the Kuga-Satake construction


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.


Wetenschappelijk artikel


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





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)


J.M. Commelin BSc


01/09/2013 tot 01/09/2017