On s'intéressera particulièrement au groupe de Chow réduit des zéro-cycles.
On commence par noter que l'application de ce groupe vers les points
rationnels de l'Albanese n'est pas forcément surjective. On s'intéresse
ensuite à la torsion du noyau de diverses applications cycles, dont l'application
cycle de Jannsen à valeurs dans la cohomologie étale continue.
On passe en revue des...
Suite à des travaux de Beilinson, T. Saito a développé la notion de cycle
caractéristique d'un faisceau étale F sur une variété algébrique lisse Y
sur un corps k algébriquement clos : il s'agit d'un cycle sur le fibré
cotangent de Y qui permet de mesurer le défaut d'acyclicité de F. Dans un
travail en commun avec Fabrice Orgogozo, étant donné un faisceau étale
constructible F de...
We’ll review some properties of rigid local systems, what we know and what we expect. Based on joint work with Michael Groechening (and for one point with Johan de Jong).
The theory of motives with modulus was introduced as a generalization of Voevodsky's theory of motives. This generalization aims to get a motivic picture of non-A^1-homotopy invariant phenomena, which cannot be captured by Voevodsky's theory. In this talk, I will briefly review the basics of the theory, and explain the construction of Hodge realization of motives with modulus, based on the...
The first counterexamples to the integral Hodge conjecture,
due to Atiyah and Hirzebruch, exploit the action of Steenrod operations.
In this talk, we will further study the interaction of Steenrod
operations and algebraic classes, over arbitrary fields, and we will
derive new examples of non-algebraic cohomology classes.
We prove that for any rationally connected threefold X over the complex numbers, there exists a smooth projective surface S and a family of 1-cycles on X parameterized by S, inducing an Abel-Jacobi isomorphism Alb(S)≅J^3(X). This statement was previously known for some classes of smooth Fano threefolds.
Let X be a smooth algebraic variety (over a field of characteristic zero) endowed with a multiplicative action of the affine line. In a recent work with Julien Sebag we show that the nearby motivic sheaf functor of a weighted equivariant function on X commutes with direct images for twists (by some Thom equivalence) of constant motives. In this talk, I will sketch the proof of this result and...
This talk will define various modules that occur in Iwasawa theory over different p-adic Lie extensions and provide a survey of recent results and open conjectures.
Looking for a category to represent Hodge filtration, with or without log, with or without modulus.
Using a geometric definition of logarithmic Hochschild homology of derived pre-log rings, we construct an André-Quillen type spectral sequence and show a logarithmic version of the Hochschild-Kostant-Rosenberg theorem. We use this to show that (log) Hochschild homology is representable in the category of log motives. Among the applications, we deduce a residue sequence for Hochschild homology...
Binda-Rulling-Saito proved that a smooth proper variety with universally trivial Chow group of zero-cycles has trivial unramified cohomology for any reciprocity sheaves.
We generalize this result to P^1-invariant sheaves with transfers. A key ingredient is a new moving lemma.
This is joint work with Wataru Kai and Shusuke Otabe.
Early on in the development of Gromov-Witten theory, Ellingsrud and Strømme computed the number of twisted cubic curves on hypersurfaces and complete intersections of appropriate (multi-)degree. With Sabrina Pauli, we adapt their method to give a refinement to a ``count’ landing in the Grothendieck-Witt ring of quadratic forms; the rank recovers the classical count, while the signature gives...
Soit X une variété algébrique réelle lisse de dimension d. On sait depuis Artin que -1 est somme de carrés dans le corps de fonctions de X si et seulement si X n'a pas de point réel. Dans ce cas, combien de carrés sont-ils nécessaires pour écrire -1 comme somme de carrés ? Nous exhibons un lien entre cette question et la géométrie et la cohomologie de X, en montrant que la borne supérieure...
Pour les algèbres simples centrales d'exposant 2, nous discuterons la notion de décomposition adaptée à certaines extensions multiquadratiques du centre. Le cas d’un corps de caractéristique 2 et de 2-dimension cohomologique 2 sera particulièrement étudié en mettant le lien avec des questions sur les formes quadratiques et la cohomologie de Kato. (C’est un travail en commun avec Demba Barry).
In a joint work with Bruno Kahn we construct a universal
Weil cohomology for smooth projective varieties over a field.
In this talk we explain universal cohomology theories as solutions of
representability problems providing the main ingredients for this
construction.
