79 citations · 567 across the 32 of their papers we have counts for
14 papers · 1 filter
-trivial Galois cohomology classes and cohomological -dimension
Charles De Clercq
Given a prime , a field of characteristic different from and a finite -primary Galois module , a Galois cohomology class in is called -trivial if it…
Isotropic localizations of mixed initial motives
Charles De Clercq, Fabio Tanania
In this paper, we define the triangulated category of initial motives, which contains, for example, all motives of projective homogeneous varieties for semisimple algebraic groups…
Effective Bialynicki-Birula-Brosnan motivic decompositions
Charles De Clercq
Let be an isotropic reductive group and be a projective -homogeneous variety. Using results from Bialynicki-Birula, Hesselink and Iversen, Brosnan showed that if is…
A-upper motives of reductive groups
Charles De Clercq, Nikita Karpenko, Anne Quéguiner-Mathieu
Given a prime number , we perform the study of Chow motives and motivic decompositions, with coefficients in , of projective homogeneous varieties for $p…
Higher Tate traces of Chow motives
Charles De Clercq, Anne Quéguiner-Mathieu
We establish the complete classification of Chow motives of projective homogeneous varieties for -inner semi-simple algebraic groups, with coefficients in $\mathbb{Z}/p\mathbb{Z…
Smooth profinite groups, III: the Smoothness Theorem
Charles De Clercq, Mathieu Florence
Let be a prime. In this article, we prove the Smoothness Theorem, which asserts that a -cyclotomic pair is -cyclotomic, for all . In the particular case…
Smooth profinite groups, I: geometrizing Kummer theory
Charles De Clercq, Mathieu Florence
In this series of three papers, we introduce and study cyclotomic pairs and smooth profinite groups. They are a geometric axiomatisation of Kummer theory for fields, with coefficie…
Lifting low-dimensional local systems
Charles De Clercq, Mathieu Florence
Let be a field of characteristic . Denote by the ring of truntacted Witt vectors of length , built out of . In this text, we consider the following q…
Lifting vector bundles to Witt vector bundles
Charles De Clercq, Mathieu Florence, Giancarlo Lucchini Arteche
Let be a scheme. Let be an integer. Denote by the scheme of Witt vectors of length , built out of . We are concerned with the question of extending (=…
On the Tits p-indexes of semisimple algebraic groups
Charles De Clercq, Skip Garibaldi
The first author has recently shown that semisimple algebraic groups are classified up to motivic equivalence by the local versions of the classical Tits indexes over field extensi…
Upper motives of products of projective linear groups
Charles De Clercq
Fix a base field F, a finite field K and consider a sequence of central simple F-algebras A_1,...,A_n. In this note we provide some results toward a classification of the indecompo…
Motivic rigidity of Severi-Brauer varieties
Charles De Clercq
Let D be a central division algebra over a field F. We study in this note the rigidity of the motivic decompositions of the Severi-Brauer varieties of D, with respect to the ring o…
Motivic decompositions of projective homogeneous varieties and change of coefficients
Charles De Clercq
We prove that under some assumptions on an algebraic group , indecomposable direct summands of the motive of a projective -homogeneous variety with coefficients in $\mathbb{F…
A going down theorem for Grothendieck Chow motives
Charles De Clercq
Let X be a geometrically split, geometrically irreducible variety over a field F satisfying Rost nilpotence principle. Consider a field extension E/F and a finite field K. We provi…