Mathematical Research Letters

Volume 25 (2018)

Number 1

A note on the Schur-finiteness of linear sections

Pages: 237 – 253



Gonçalo Tabuada (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.; Departamento de Matemática & Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal)


Making use of the recent theory of noncommutative motives, we prove that Schur-finiteness in the setting of Voevodsky’s mixed motives is invariant under homological projective duality. As an application, we show that the mixed motives of smooth linear sections of certain (Lagrangian) Grassmannians, spinor varieties, and determinantal varieties, are Schur-finite. Finally, we upgrade our applications from Schur-finiteness to Kimura-finiteness.

2010 Mathematics Subject Classification

14A22, 14C15, 14M12, 14M15, 18D20, 18E30

The author was supported by the National Science Foundation CAREER Award #1350472 and by the Portuguese Foundation for Science and Technology grant PEst-OE/MAT/UI0297/2014.

Received 24 October 2016

Accepted 14 March 2017

Published 4 June 2018