12 citations · 12 across the 10 of their papers we have counts for
10 papers
Homotopy coherent Gysin functoriality
Frédéric Déglise, Niels Feld, Fangzhou Jin
We construct homotopy coherent Gysin pullbacks for weak Borel-Moore theories on smooth schemes, addressing the higher coherence problem for Gysin morphisms associated with closed i…
Homological Milnor-Witt modules and Chow-Witt groups over general bases
Frédéric Déglise, Niels Feld, Fangzhou Jin
We introduce a general theory of homological Milnor-Witt cycle modules over an excellent base scheme equipped with a dimension function, extending both Rost's cycle modules and Fel…
Motivic homotopy theory and stable homotopy groups
Frédéric Déglise
These notes, written version of a Bourbaki talk, survey Morel-Voevodsky's motivic homotopy theory over a field, with a focus on computations of motivic homotopy sheaves, both stabl…
Spectral sequences in unstable higher homotopy theory and applications to the coniveau filtration
Frédéric Déglise, Rakesh Pawar
With the aim of understanding Morel's result on the -homotopy sheaves over a field, we extend the theory of unstable spectral sequences of Bousfield and Kan in the $\…
Generic motives and motivic cohomology of fields
F. Déglise
This paper investigates the structure of generic motives and their implications for the motivic cohomology of fields. Originating in Voevodsky's theory of motives and related to Be…
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…
Notes on Milnor-Witt K-theory
Frédéric Déglise
These notes develop the foundations of Milnor-Witt K-theory for fields of arbitrary characteristic, without any perfectness assumptions. Extending the work of Morel and Feld, we es…
Moving lemmas and the homotopy coniveau tower
Frédéric Déglise, Niels Feld, Fangzhou Jin
In this note we study the functoriality of the coniveau filtration in motivic homotopy theory via a moving lemma over a base scheme, extending previous works of Levine and Bachmann…
The rigid syntomic ring spectrum
Frédéric Déglise, Nicola Mazzari
The aim of this paper is to show that Besser syntomic cohomology is representable by a rational ring spectrum in the motivic homotopical sense. In fact, extending previous construc…
Around the Gysin triangle I
Frédéric Déglise
We define and study Gysin morphisms on mixed motives over a perfect field. Our construction extends the case of closed immersions, already known from results of Voevodsky, to arbit…