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Some remarks concerning Voevodsky’s nilpotence conjecture

Marcello Bernardara, Matilde Marcolli and Gonçalo Tabuada


In this article we extend Voevodsky’s nilpotence conjecture from smooth projective schemes to the broader setting of smooth proper dg categories. Making use of this noncommutative generalization, we then address Voevodsky’s original conjecture in the following cases: quadric fibrations, intersection of quadrics, linear sections of Grassmannians, linear sections of determinantal varieties, homological projective duals, and Moishezon manifolds.

Funding source: National Science Foundation

Award Identifier / Grant number: CAREER Award #1350472

Award Identifier / Grant number: DMS-1201512

Award Identifier / Grant number: PHY-1205440

Funding statement: G. Tabuada was partially supported by the National Science Foundation CAREER Award #1350472 and by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project grant UID/MAT/00297/2013 (Centro de Matemática e Aplicações). M. Marcolli was partially supported by the NSF grants DMS-1201512 and PHY-1205440.


The authors are grateful to Bruno Kahn and Claire Voisin for useful comments and answers, as well as to the anonymous referee for useful remarks.


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Received: 2014-11-21
Published Online: 2015-11-28
Published in Print: 2018-5-1

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