17 citations · 79 across the 21 of their papers we have counts for
21 papers
Essential p-dimension and Chern numbers
Olivier Haution
Let be a smooth, projective, geometrically connected variety over a field containing a root of unity of order . If has a Chern number prime to , we show that ever…
Dimension of fixed loci of diagonalizable groups via algebraic cobordism
Olivier Haution
We determine all restrictions on the dimension of the fixed locus of a diagonalizable group acting on a smooth projective variety that arise from the Chern numbers of the ambient v…
On the first Steenrod square for Chow groups
Olivier Haution
We construct a weak version of the homological first Steenrod square, a natural transformation from the modulo two Chow group to the Chow group modulo two and two-torsion. No assum…
Actions of diagonalizable -groups and Chern numbers modulo
Olivier Haution
We obtain lower bounds for the dimension of fixed loci of diagonalizable -groups acting on smooth projective varieties. Those bounds depend on the modulo Chern numbers of th…
The geometric concentration theorem
Olivier Haution
We establish a purely geometric form of the concentration theorem (also called localization theorem) for actions of a linearly reductive group on an affine scheme over an a…
Odd rank vector bundles in eta-periodic motivic homotopy theory
Olivier Haution
We observe that, in the eta-periodic motivic stable homotopy category, odd rank vector bundles behave to some extent as if they had a nowhere vanishing section. We discuss some con…
Motivic Pontryagin classes and hyperbolic orientations
Olivier Haution
We introduce the notion of hyperbolic orientation of a motivic ring spectrum, which generalises the various existing notions of orientation (by the groups GL, SLc, SL, Sp). We show…
On the algebraic cobordism ring of involutions
Olivier Haution
We consider the cobordism ring of involutions of a field of characteristic not two, whose elements are formal differences of classes of smooth projective varieties equipped with an…
The stable Adams operations on Hermitian K-theory
Jean Fasel, Olivier Haution
We prove that exterior powers of (skew-)symmetric bundles induce a -ring structure on the ring , when is a scheme where is invertible. Using this…
Connective K-theory and Adams operations
Olivier Haution, Alexander S. Merkurjev
We investigate the relations between the Grothendieck group of coherent modules of an algebraic variety and its Chow group of algebraic cycles modulo rational equivalence. Those ar…
Involutions and Chern numbers of varieties
Olivier Haution
Consider an involution of a smooth projective variety over a field of characteristic not two. We look at the relations between the variety and the fixed locus of the involution fro…
Fixed point theorems involving numerical invariants
Olivier Haution
We exhibit invariants of smooth projective algebraic varieties with integer values, whose nonvanishing modulo p prevents the existence of an action without fixed points of certain…
Diagonalisable p-groups cannot fix exactly one point on projective varieties
Olivier Haution
We prove an algebraic version of a classical theorem in topology, asserting that an abelian p-group action on a smooth projective variety of positive dimension cannot fix exactly o…
On rational fixed points of finite group actions on the affine space
Olivier Haution
Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, i…
Involutions of varieties and Rost's degree formula
Olivier Haution
To an algebraic variety equipped with an involution, we associate a cycle class in the modulo two Chow group of its fixed locus. This association is functorial with respect to prop…
Detection by regular schemes in degree two
Olivier Haution
Using Lipman's results on resolution of two-dimensional singularities, we provide a form of resolution of singularities in codimension two for reduced quasi-excellent schemes. We d…
Invariants of upper motives
Olivier Haution
Let H be a homology theory for algebraic varieties over a field k. To a complete k-variety X, one naturally attaches an ideal of the coefficient ring H(k). We show that, when X is…
Integrality of the Chern character in small codimension
Olivier Haution
We prove an integrality property of the Chern character with values in Chow groups. As a consequence we obtain, for a prime number p, a construction of the p-1 first homological St…
Degree formula for the Euler characteristic
Olivier Haution
We give a proof of the degree formula for the Euler characteristic previously obtained by Kirill Zainoulline. The arguments used here are considerably simpler, and allow us to remo…
Duality and the topological filtration
Olivier Haution
We investigate some relations between the duality and the topological filtration in algebraic K-theory. As a result, we obtain a construction of the first Steenrod square for Chow…
Reduced Steenrod operations and resolution of singularities
Olivier Haution
We give a new construction of a weak form of Steenrod operations for Chow groups modulo a prime number p for a certain class of varieties. This class contains projective homogeneou…