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You are here: FRIAS Fellows Fellows 2019/20 Prof. Dr. Frédéric Déglise

Prof. Dr. Frédéric Déglise

Institut Mathématique de Bourgogne
External Senior Fellow
Marie S. Curie FCFP Fellow
November 2017 - March 2018


I defended my Ph. D. in 2002 in Paris 7 under the supervision of F. Morel and my Habilitation thesis in 2010 in Paris 13. Since 2016, I am Directeur de recherche at the CNRS, working in the IMB at Dijon.
My field of research is motivic homotopy theory, from motives and algebraic cycles to abstract homotopy and its methods. My work has been focused on the development and study of cohomology theories, mainly motivic cohomology, but more generally cohomologies coming from Morel-Voevodsky's A1-homotopy category. The orientation theory known in algebraic topology can be transported to A1-homotopy and gives rise to the study of characteristic classes, duality, Gysin morphisms and purity.
My recent researches have been directed towards the following topics on triangulated motives over arbitrary bases: the integral coefficients case, the construction of t-structures (called homotopy t-structures) and the relationship with p-adic Hodge theory via syntomic cohomology.

Selected Publications

  • M. Bondarko, F. Déglise. Dimensional homotopy t-structures in motivic homotopy theory. Adv. Math., 311: 91-189, 2017.
  • D.-C. Cisinski and F. Déglise. Integral mixed motives in equal characteristics. Doc. Math., (Extra volume: Alexander S. Merkurjev's sixtieth birthday): 145-194, 2015.
  • D.-C. Cisinski and F. Déglise. Etale motives. Compos. Math., 152(3): 556-666, 2016.
  • F. Déglise. Orientable homotopy modules. Am. Journ. of Math., 135(2): 519-560, 2013.
  • D.-C. Cisinski and F. Déglise. Mixed weil cohomologies. Adv. in Math., 230(1): 55-130, 2012

FRIAS Research Project

Homotopy t-structure and a Leray-type spectral sequence

In this research project, part of a bigger research program that I have made to compete in a Directeur de recherche position at the CNRS in France, I propose to develop a tool that hopefully will help to get new computations of the so-called motivic cohomology. More precisely, I propose to study a new spectral sequence which is inspired by the Leray spectral sequence, whose usefulness and versatility is universally acknowledge, in every branches of mathematics that uses cohomology. This go through the general concept of t-structures, introduced by Beilinson, Bernstein and Deligne and its application to motivic complexes whose first appearance is due to Voevodsky, and was developed further in several works by Morel, Ayoub and finally Bondarko and Déglise. After Voevodsky, this structure is called the homotopy t-structure. The first task that I proposed to undertake is to study special objects induced by that t-structure, of a grouplike nature, the objects of the heart. This is a first step in order to determine and compute a spectral sequence that arises naturally from a t-structure. The second part of the program, widely open, is to start computing with the spectral sequence in special geometric situations.