Triangulated Categories of Mixed Motives

Denis-Charles Cisinski is Professor of Mathematics at the Universität Regensburg, Germany. He previously held positions at the University of Toulouse and at the University Paris XIII. His research focuses on homotopical algebra, category theory, K-theory and the cohomology of schemes. He is also the author of two monographs entitled Les préfaisceaux comme modèles des types d'homotopie (2006) and Higher Categories and Homotopical Algebra (2019).Frédéric Déglise has been Chargé de recherche in the CNRS, at the University Paris XIII from 2003 to 2011 and at the ENS Lyon from 2011 to 2016. He is since then Directeur de recherche in the CNRS, at the University of Burgundy. He has been Marie Curie Fellow at the FRIAS institute in 2017. He is a specialist of homotopy theory, algebraic geometry, motivic homotopy theory and motives.

• Introduction.- Part I Fibred categories and the six functors formalism.- Part II Construction of fibred categories.- Part III Motivic complexes and relative cycles.- Part IV Beilinson motives and algebraic K-theory.- References.- Index.- Notation.- Index of properties of P-fibred triangulated categories.

“It is obviously aimed at readers who are intimately familiar with the motivic literature. … this work is likely to become a valuable reference for researchers in the area.” (Igor A. Rapinchuk, Mathematical Reviews, September, 2020)