## arXiv Analytics

### arXiv:1710.04644 [math.AG]AbstractReferencesReviewsResources

#### Grothendieck's standard conjecture of type D in positive characteristic for linear sections of determinantal varieties

Published 2017-10-12Version 1

Making use of topological periodic cyclic homology, we extend Grothendieck's standard conjecture of type D (with respect to crystalline cohomology theory) from smooth projective schemes to smooth proper dg categories in the sense of Kontsevich. Among other applications, we prove Grothendieck's original conjecture in the new cases of linear sections of determinantal varieties. Along the way, we establish similar results for Grothendieck's standard conjecture of type C+ (a.k.a. the sign conjecture).