Cisinski, Denis-Charles; Déglise, Frédéric
Integral mixed motives in equal characteristic
Doc. Math. (Bielefeld) Extra Vol. Alexander S. Merkurjev's Sixtieth Birthday, 145-194 (2015)
For noetherian schemes of finite dimension over a field of characteristic exponent $p$, we study the triangulated categories of $\bold Z[1/p]$-linear mixed motives obtained from cdh-sheaves with transfers. We prove that these have many of the expected properties. In particular, the formalism of the six operations holds in this context. When we restrict ourselves to regular schemes, we also prove that these categories of motives are equivalent to the more classical triangulated categories of mixed motives constructed in terms of Nisnevich sheaves with transfers. Such a program is achieved by comparing these various triangulated categories of motives with modules over motivic Eilenberg-MacLane spectra.
Mathematics Subject Classification
19E15, 14C15, 14C25, 14F20, 14F42
mixed motives, Nisnevich topology, integral motivic cohomology, higher Chow groups, l-adic independency, cdh-topology