Séminaires : Séminaire des Thésards

Le séminaire des thésards est l'occasion pour les doctorants de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Un mercredi sur deux à 18h00, en alternance entre Jussieu et Sophie Germain.

Intersection theory, which aims at understanding precisely how algebraic varieties intersect, is an old research subject in algebraic geometry, and it is nowadays well understood. However, it does not generalize well to the arithmetic case. Arithmetic intersection theory, developed by Gillet and Soulé in the 90s, strikingly mixes the previous algebraic objects at finite places, and complex analytic objects called Green currents. This asymmetry motivates the search for non-Archimedean Green currents, with the objective of unifying both finite and infinite places.

During this presentation, I will present the basic constructions of classical intersection theory, then discuss in more detail the notion of Green currents and the arithmetic theory. Finally, I will briefly present ongoing approaches that tend towards a non-Archimedean version.