Statut  Confirmé 
Série  MATHIHES 
Domaines  hepth 
Date  Jeudi 21 Mars 2019 
Heure  14:30 
Institut  IHES 
Salle  Amphithéâtre Léon Motchane 
Nom de l'orateur  Kontsevitch 
Prenom de l'orateur  Maxim 
Addresse email de l'orateur  
Institution de l'orateur  IHES 
Titre  Bridgeland Stability over NonArchimedean Fields (2/4) 
Résumé  Bridgeland stability structure/condition on a triangulated category is a vast generalization of the notion of an ample line bunlde (or polarization) in algebraic geometry. The origin of the notion lies in string theory, and is applicable to derived categories of coherent sheaves, quiver representations and Fukaya categories. In a category with Bridgeland stability every objects carries a canonical filtration with semistable pieces, an analog of HarderNarasimhan filtration. It is expected that for categories over complex numbers Bridgeland stability structures often admit analytic enhancements, similar to the relation between ample bundles and usual Kaehler metrics. In a sense, this should be a generalization DonaldsonUhlenbeckYau theorem which syas that a holomorphic vector bundle over compact Kaehler manifold is polystable if and only if it admits a metrization satisfying hermitean YangMills equation. In my course I will talk about a nonarchimedean analog of analytic Bridgeland stability. I will show several examples, results and conjectures. In particular, I'll introduce nonarchimedean moment map equations, generalized honeycomb diagrams, and hypothetical stability on derived categories of coherent sheaves on maximally degenerating varieties over nonarchimedean fields. 
Numéro de preprint arXiv  
Commentaires  Cours de l'IHES 
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