Stefan Schreieder

Title: Algebraic cycles and refined unramified cohomology

Abstract: 
I will introduce refined unramified cohomology groups. This notion allows to give in arbitrary 
degree a cohomological interpretation of the failure of integral Hodge or Tate-type conjectures, 
of l-adic Griffiths groups, and of the subgroup of the Griffiths group that consists of torsion 
classes with trivial transcendental Abel-Jacobi invariant. This simplifies and generalizes previous 
results of Bloch-Ogus, Colliot-Thelene–Voisin, Voisin, and Ma that concerned cycles of codimension 
two or three. As an application, we get for any i>2 the first example of a uniruled smooth complex 
projective variety for which the Hodge conjecture fails for codimension i-cycles in a way that cannot 
be explained by the failure on any lower-dimensional variety.