A note on Grothendieck’s standard conjectures of type C⁺ and D
Name
S0002-9939-2018-13955-6.pdf
Size
243.52 KB
Format
Adobe PDF
Checksum (MD5)
b412552a0e7b123cbd191c2feba8879e
Author(s)
Trigo Neri Tabuada, Goncalo Jorge
Date Issued
January 2018
Journal
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Tabuada, Gonçalo. “A note on Grothendieck’s standard conjectures of type C⁺ and D.” Proceedings of the American Mathematical Society 146, 4 (January 12, 2018): 1389–1399 © 2018 American Mathematical Society
Version
Final published version
Abstract
Grothendieck conjectured in the sixties that the even Künneth projector (with respect to a Weil cohomology theory) is algebraic and that the homological equivalence relation on algebraic cycles coincides with the numerical equivalence relation. In this note we extend these celebrated conjectures from smooth projective schemes to the broad setting of smooth proper dg categories. As an application, we prove that Grothendieck's conjectures are invariant under homological projective duality. This leads to a proof of Grothendieck's original conjectures in the case of intersections of quadrics and linear sections of determinantal varieties. Along the way, we also prove the case of quadric fibrations and intersections of bilinear divisors.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1090/PROC/13955
