Making use of homological projective duality and the recent theory of (Jacobians of) noncommutative Chow motives, we compute the rational Chow groups of a complete intersection of either two quadrics or three odd-dimensional quadrics. We show moreover that the unique non-trivial algebraic Jacobians are the middle ones. As a first application, we describe the rational Chow motives of these complete intersections. As a second application, we prove that smooth fibrations in such complete intersections over small dimensional bases S verify Murre's conjecture (dim(S) less or equal to 1), Grothendieck's standard conjectures (dim(S) less of equal to 2), and Hodge's conjecture (dim(S) less or equal to 3).
Publié le : 2016-07-05
Classification:
intersection of quadrics,
semiorthogonal decompositions,
noncommutative motives,
Chow groups,
intermediate Jacobians,
14A22, 14C15, 14F05, 14J40, 14M10,
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],
[MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT],
[MATH.MATH-KT]Mathematics [math]/K-Theory and Homology [math.KT],
[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]
@article{hal-00876512,
author = {Bernardara, Marcello and Tabuada, Goncalo},
title = {Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives},
journal = {HAL},
volume = {2016},
number = {0},
year = {2016},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00876512}
}
Bernardara, Marcello; Tabuada, Goncalo. Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives. HAL, Tome 2016 (2016) no. 0, . http://gdmltest.u-ga.fr/item/hal-00876512/