Séminaires : Autour des cycles algébriques

Equipe(s) : fa, tn,
Responsables :A. Cadoret - F. Charles - J. Fresán - M. Morrow
Email des responsables : anna.cadoret@imj-prg.fr; matthew.morrow@imj-prg.fr; francois.charles@math.u-psud.fr; javier.fresan@polytechnique.edu
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Orateur(s) Oliver Braunling, Kęstutis Česnavičius et Adam Topaz - ,
Titre Séminaire Autour des cycles algébriques
Horaire14:00 à 18:00
Résume14h00--15h00 : Oliver Braunling (Universität Freiburg) K-theory of locally compact modules
We discuss the K-theory of categories of modules over a number field, but additionally equipped with a locally compact topology. Although this is not an abelian category, such a category has a natural exact structure, and Pontryagin duality makes it an exact category with duality. Generalizing results of Dustin Clausen, we explain how to compute the K-theory of such categories, and how it is connected to the adeles and other number-theoretical objects. Joint with Peter Arndt.

15h30--16h30 : Kęstutis Česnavičius (Université Paris-Sud, CNRS) Grothendieck--Lefschetz for vector bundles
According to the Grothendieck--Lefschetz theorem from SGA 2, there are no nontrivial line bundles on the punctured spectrum U_R of a local ring R that is a complete intersection of dimension ≥4. Hailong Dao isolated a condition on a vector bundle V of arbitrary rank on U_R, always satisfied by a line bundle, and conjectured that its validity is necessary and sufficient for V to be trivial. We use deformation theoretic techniques to settle Dao's conjecture and present examples showing that its assumptions are sharp.

17h00--18h00 : Adam Topaz (University of Oxford) Recovering function fields from their ℓ-adic cohomology
This talk will present some recent work in progress which shows that the function field of a higher-dimensional variety is determined, up-to isomorphism, from its ℓ-adic cohomology ring, when it is endowed with the Galois action of a "sufficiently global" base field. A comparison with Bogomolov's programme and the Bogomolov-Pop conjecture in birational anabelian geometry will also be discussed.