Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives
Name
Tabuada_Chow groups.pdf
Size
206.32 KB
Format
Adobe PDF
Checksum (MD5)
27d5b4b384b04924ce00f08654e34ef9
Author(s)
Bernardara, M.
Trigo Neri Tabuada, Goncalo Jorge
Date Issued
July 2016
Journal
Izvestiya: Mathematics
Publisher
Turpion
Citation
Bernardara, M., and G. Tabuarda. "Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives." Izvestiya: Mathematics, Volume 80, Number 3 (2016), pp. 463-480.
Version
Original manuscript
Abstract
Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when dim(S) [less than or equal to] 1), Grothendieck's standard conjecture of Lefschetz type (when dim(S) [less than or equal to] 2), and Hodge's conjecture (when dim(S) [less than or equal to] 3).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1070/IM8409
