Birational motives, II: Triangulated birational motives

Abstract

We develop birational versions of Voevodsky's triangulated categories of motives over a field, and relate them with the pure birational motives studied in arXiv:0902.4902 [math.AG]. We also get an interpretation of unramified cohomology in this framework, leading to "higher derived functors of unramified cohomology".

Compared to the initial version: previous Subsection 4.2 has been upgraded to Section 5; previous Lemmas 5.2.5 and 5.2.6 have been corrected to Proposition 6.2.5 and Lemma 6.2.6; at the referee's request, previous Appendix B and the proof of previous Proposition C.1.1 (now A.4.1) have been removed (please consult the initial version for them)

References in corpus (1)

• Compact Corigid Objects in Triangulated Categories and Co-t-structures

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• On Chow-pure cohomology and Euler characteristics for motives and varieties, and their relation to unramified cohomology and Brauer groups
• Derived Log Albanese Sheaves
• An $l$-adic norm residue epimorphism theorem
• Universal birational invariants and ${\mathbb{A}}^1$-homology
• Unramified logarithmic Hodge-Witt cohomology and ${\mathbb{P}}^1$-invariance
• Torsion birational motives of surfaces and unramified cohomology