Une journée Géométrie algébrique et théorie des nombres en Bourgogne Franche-Comté est organisée le vendredi 5 avril 2024, à Besançon, LmB, salles 316B et 316Bbis.
La journée commencera par deux exposées pléniers proposés par Hassan Oukhaba (LmB) et Keyao Peng (IMB), et se poursuivra par 5 exposés dispensés par des jeunes chercheurs du LmB et de l’IMB.
PROGRAMME
- 9h45-10h45 : Hassan Oukhaba (LmB), Autour du demi-plan de Drinfeld
- 10h45-11h45 : Keyao Peng (IMB), MW-motivic cohomology of linear algebraic groups and Stiefel varieties
Abstract
We present some computations in MW-motivic cohomology. Following the classical computations and using the analogue in A1-homotopy of the Leray spectral sequence, we compute the (η-inverted) MW-motivic cohomology of linear algebraic groups and Stiefel varieties, obtaining, in particular, the computation of the (η-inverted) MW-motivic cohomology of the symplectic groups Sp2n and the general linear groups GLn. We also make a conjecture on the MW-motivic cohomology of Stiefel varieties.
- 11H45-12h15 : Crislaine Kuster (IMB), Foliations on homogeneous varieties
Abstract
Let X be a projective homogeneous variety, i.e. varieties which admit a Lie group acting on it transitively. The projective space and grassmannians are examples of such varieties. Consider an embedding of X in a projective space P^n. In this talk, I will present a survey on the theory of foliations on homogeneous varieties. In particular, we will be interested in whether a foliation on X is a restriction of a foliation on the ambient space P^n or not.
- 13h45-14h15, 2 présentations de 15 mn :
- Victor Chachay (IMB), Generalizing the count of 27 lines in the motivic setting
Abstract
I’ll introduce a geometrical way to count the 27 lines of a cubic surface to illustrate how we try to use this as reference for generalizing this constant to an enumerative invariant on other Del Pezzo surfaces over any field (hopefully). - Felipe Monteiro (IMB), Logarithmic tangent sheaves on complete intersections
Abstract
Logarithmic tangent sheaves associated to polynomials can be classically defined as kernels of the map induced by the gradient of these polynomials. Following the work of D. Faenzi, we investigate possible generalizations of the classical theory of logarithmic tangent sheaves for a regular sequence of polynomials, considering the Jacobian matrix associated. From this generalization, new behaviours appear, as the dependence of choice of generators of a regular sequence, and the behaviours of the classical setting such as stability and freeness properties can be generalized in this setting. This presentation will briefly review some of the aspects of the classical theory of logarithmic tangent sheaves of divisors, to then make some comments between the generalized setting for complete intersections.
- Victor Chachay (IMB), Generalizing the count of 27 lines in the motivic setting
- 14h15-14h45 : Marsaut Chabat (LmB), Théorie d’Iwasawa des surfaces abéliennes
Résumé
Certaines conséquences attendues de la théorie d’Iwasawa concernent la conjecture de Birch et Swinerton-Dyer sur les variétés abéliennes. On commencera par expliquer cela. On verra ensuite comment la géométrie des variétés de Siegel fournis de puissants outils pour attaquer ces conjectures. - Pause
- 15h10-15h40 : Ivan Rosas Soto (IMB), Décomposition de motifs étale intégraux, degré étale et 0-cycles
Résumé
Nous discuterons des problèmes de décomposition des motifs de Chow à coefficients intégraux, en particulier pour les variétés sans 0-cycles de degré 1. Dans cet exposé, nous définirons la version étale de l’application degré et donnerons quelques exemples de variétés projectives lisses sur un corps de dimension cohomologique 1 sans 0-cycles de degré un mais avec un 0-cycles étale de degré 1. - 15h40-16h10 : Victor Cordeiro (IMB), Foliation by curves in P^3
Abstract
Given a smooth variety X, a foliation by curves on X is given by a subsheaf of TX, the tangent sheaf of X. In this talk we will discuss some properties of foliation by curves, the classification in degree 0 and 1 and what we could show for degree 2.
Organisateurs : Christine Huyghe (LmB) et Daniele Faenzi (IMB)
Cette rencontre bénéficie du soutien de la Fédération Bourgogne Franche-Comté Mathématiques.