53 citations · 322 across the 36 of their papers we have counts for
45 papers
Vector bundles on singular surfaces and threefolds
Jean Fasel, Maria Yakerson
We fully classify vector bundles of critical rank on normal affine surfaces and threefolds over algebraically closed fields via their Chern classes. We also prove existence of rank…
Suslin's cancellation conjecture on smooth real affine varieties with few real points
Sourjya Banerjee, Jean Fasel, Samuel Lerbet
We study Suslin's cancellation conjecture on smooth real affine varieties whose real locus is empty or, more generally, of small cohomological dimension.
Exotic Hopf maps, weight shifting and applications to vector bundles
Jean Fasel, William Hornslien
Using motivic homotopy theory we produce several explicit polynomial representatives of the suspension of the Hopf map defined over the integers. We derive from this computation an…
Splitting vector bundles over real algebraic varieties
Aravind Asok, Jean Fasel, Samuel Lerbet
Suppose is a smooth affine real variety and is a vector bundle over . We analyze the problem of splitting off a free rank one summand from in cor…
Quadratic Riemann-Roch formulas
Frédéric Déglise, Jean Fasel
In this article, we produce Grothendieck-Riemann-Roch formulas for cohomology theories that are not oriented in the classical sense. We then specialize to the case of cohomology th…
On Tate Milnor-Witt Motives
Jean Fasel, Nanjun Yang
Smooth projective -varieties with isolated rational fixed points admit Tate Milnor-Witt motives. Over Euclidean fields, we give a splitting formula of such motives, w…
Formal ternary laws and Buchstaber's 2-groups
David Coulette, Frédéric Déglise, Jean Fasel +1
We develop the algebraic formalism of the formal ternary laws of C. Walter and we compare them to Buchstaber's 2-valued formal group laws. We also compute the "elementary" formal t…
Vector bundles on algebraic varieties
Aravind Asok, Jean Fasel
We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.
Suslin's cancellation conjecture in the smooth case
Jean Fasel
We prove that stably isomorphic vector bundles of rank d-1 on a smooth affine d-fold X over an algebraically closed field k are indeed isomorphic, provided d! is invertible in k. T…
Algebraic vector bundles and -local A^1-homotopy theory
Aravind Asok, Jean Fasel, Michael J. Hopkins
Using techniques of A^1-homotopy theory, we produce motivic lifts of elements in classical homotopy groups of spheres; these lifts provide polynomial maps of spheres and allow us t…
On the rational motivic homotopy category
Frédéric Déglise, Jean Fasel, Adeel A. Khan +1
We study the structure of the rational motivic stable homotopy category over general base schemes. Our first class of results concerns the six operations: we prove absolute purity,…
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…
Milnor-Witt Motives
Tom Bachmann, Baptiste Calmès, Frédéric Déglise +2
We develop the theory of Milnor-Witt motives and motivic cohomology. Compared to Voevodsky's theory of motives and his motivic cohomology, the first difference appears in our defin…
Lectures on Chow-Witt groups
Jean Fasel
In these lectures, we provide a toolkit to work with Chow-Witt groups, and more generally with the homology and cohomology of the Rost-Schmid complex associated to Milnor-Witt -…
Localization and nilpotent spaces in A^1-homotopy theory
Aravind Asok, Jean Fasel, Michael J. Hopkins
For a subring of the rational numbers, we study -localization functors in the local homotopy theory of simplicial presheaves on a small site and then in -homo…
The Borel character
Frédéric Déglise, Jean Fasel
The main purpose of this article is to define a quadratic analog of the Chern character, the so-called Borel character, which identifies rational higher Grothendieck-Witt groups wi…
Borel isomorphism and absolute purity
Frédéric Déglise, Jean Fasel, Fangzhou Jin +1
We prove absolute purity for the rational motivic sphere spectrum. The main ingredient is the construction of an analogue of the Chern character, where algebraic K-theory is replac…
Rank weights for arbitrary finite field extensions
Grégory Berhuy, Jean Fasel, Odile Garotta
In this paper, we study several definitions of generalized rank weights for arbitrary finite extensions of fields. We prove that all these definitions coincide, generalizing known…
Motivic spheres and the image of the Suslin--Hurewicz map
Aravind Asok, Jean Fasel, Ben Williams
We show that an old conjecture of A.A. Suslin characterizing the image of a Hurewicz map from Quillen K-theory in degree to Milnor K-theory in degree admits an interpretati…
On the effectivity of spectra representing motivic cohomology theories
Tom Bachmann, Jean Fasel
Let k be an infinite perfect field. We provide a general criterion for a spectrum in the stable homotopy category over k to be effective, i.e. to be in the localizing subcategory g…
The Milnor-Witt motivic ring spectrum and its associated theories
Frédéric Déglise, Jean Fasel
We build a ring spectrum representing Milnor-Witt motivic cohomology, as well as its étale local version and show how to deduce out of it three other theories: Borel-Moore homology…
A comparison theorem for MW-motivic cohomology
Baptiste Calmès, Jean Fasel
We prove that for a finitely generated field over an infinite perfect field k, and for any integer n, the (n,n)-th MW-motivic cohomology group identifies with the n-th Milnor-Witt…
A cancellation theorem for Milnor-Witt correspondences
Jean Fasel, Paul Arne Østvær
We show that finite Milnor-Witt correspondences satisfy a cancellation theorem with respect to the pointed multiplicative group scheme. This has several notable applications in the…
MW-motivic complexes
Frédéric Déglise, Jean Fasel
The aim of this work is to develop a theory parallel to that of motivic complexes based on cycles and correspondences with coefficients in quadratic forms. This framework is closer…