Integral Mixed Motives in Equal Characteristic

For noetherian schemes of finite dimension over a field of characteristic exponent $p$, we study the triangulated categories of $\ZZ[1/p]$-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.

2010 Mathematics Subject Classification: 14F42, (14C15, 14C25, 14F43)

Keywords and Phrases: integral mixed motives, 6 functors formalism, modules over ring spectra, finite correspondences, integral motivic cohomology, higher Chow groups

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