Algebraic cycles and Hodge theoretic connectivity

On syzygies of projective varieties

“…This answers the question 5.13 of [3]. Here, we would like to mention that when X is a smooth variety, a vanishing theorem of M. Nori can also be used to answer this question ( [8,Proposition 3.4]). …”

Chow Rings, Decomposition of the Diagonal, and the Topology of Families

“…This will be crucial because the total space of the family X × B X is very easy to describe, while it can become very complicated after an arbitrary base change. The idea of spreading out cycles has become very important in the theory of algebraic cycles since Nori's paper [76] (see [47], [89]). For most problems however, we usually need to work over a generically finite extension of the base, due to the fact that cycles existing at the general point will exist on the total space of the family only after a base change.…”

“…The first place where it appears explicitly is Nori's paper [76], where it is shown that the cohomology class of the spread cycle governs many invariants of the cycle restricted to general fibers. The idea is the following (see also [47]): Assume that we have a family of smooth algebraic varieties, that is, a smooth surjective morphism π : X → B, INTRODUCTION weyllecturesformat September 3, 2013 6x9…”

Coniveau filtration and mixed motives

“…It can be compared with other filtrations (see [Nor93], [Fri95]). It is an interesting question whether a similar comparison to that of [Nor93,rem. 5.4] can be obtained in the case of rigid cohomology.…”