English
An overview on some recent results about $p$-adic differential equations over Berkovich curves
Post-edited
Auteurs : Pulita, Andrea (Auteur de la Conférence)
CIRM (Editeur )
12H25 - $p$-adic differential equations
14G22 - Rigid analytic geometry
CIRM (Editeur )
Résumé :
I will give an introductory talk on my recent results about $p$-adic differential equations on Berkovich curves, most of them in collaboration with J. Poineau. This includes the continuity of the radii of convergence of the equation, the finiteness of their controlling graphs, the global decomposition by the radii, a bound on the size of the controlling graph, and finally the finite dimensionality of their de Rham cohomology groups, together with some local and global index theorems relating the de Rham index to the behavior of the radii of the curve. If time permits I will say a word about some recent applications to the Riemann-Hurwitz formula.
Codes MSC : 12H25 - $p$-adic differential equations
14G22 - Rigid analytic geometry
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 06/04/17 Date de captation : 28/03/17 Sous collection : Research talks arXiv category : Number Theory Domaine : Algebraic & Complex Geometry ; PDE Format : MP4 (.mp4) - HD Audience : Researchers Download : https://videos.cirm-math.fr/2017-03-28_Pulita.mp4 
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Informations sur la Rencontre
Nom de la rencontre : $p$-adic analytic geometry and differential equations / Géométrie analytique et équations différentielles $p$-adiquesOrganisateurs de la rencontre : Lebacque, Philippe ; Nicaise, Johannes ; Poineau, Jérôme Dates : 27/03/17 - 31/03/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1609.html
Données de citation
DOI : 10.24350/CIRM.V.19153403Citer cette vidéo: Pulita, Andrea (2017). An overview on some recent results about $p$-adic differential equations over Berkovich curves. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19153403 URI : http://dx.doi.org/10.24350/CIRM.V.19153403 |
Voir aussi
- [Multi angle] Explosion of Lyapunov exponents using non-Archimedean geometry / Auteur de la Conférence Favre, Charles.
- [Multi angle] Arithmetic $D$-modules and existence of crystalline companion / Auteur de la Conférence Abe, Tomoyuki.
- [Multi angle] $D$-modules and $p$-curvatures / Auteur de la Conférence Esnault, Hélène.
- [Multi angle] de Rham theorem in non-Archimedean analytic geometry / Auteur de la Conférence Berkovich, Vladimir.
Bibliographie
- Baldassarri, F. (2010). Continuity of the radius of convergence of differential equations on $p$-adic analytic curves. Inventiones Mathematicae, 182(3), 513-584 - http://dx.doi.org/10.1007/s00222-010-0266-7
- Kedlaya, Kiran S. (2016). Convergence polygons for connections on Nonarchimedean curves. In Baker, Matthew (ed.) et al., Nonarchimedean and tropical geometry (pp. 51-97). Cham: Springer - http://dx.doi.org/10.1007/978-3-319-30945-3_3
- Kedlaya, Kiran S. (2015). Local and global structure of connections on nonarchimedean curves. Compositio Mathematica, 151, No. 6, 1096-1156 - http://dx.doi.org/10.1112/S0010437X14007830
- Kedlaya, Kiran S. (2010). $p$-adic differential equations. Cambridge: Cambridge University Press (ISBN 978-0-521-76879-5/hbk). xvii, 380 p. (2010). - http://www.cambridge.org/fr/academic/subjects/mathematics/number-theory/p-adic-differential-equations?format=HB&isbn=9780521768795
- Poineau, J., & Pulita, A. (2015). Continuity and finiteness of the radius of convergence of a $p$-adic differential equation via potential theory. Journal für die Reine und Angewandte Mathematik, 707, 125-147 - http://dx.doi.org/10.1515/crelle-2013-0086
- Poineau, J., & Pulita, A. (2015). The convergence Newton polygon of a $p$-adic differential equation. II: Continuity and finiteness on Berkovich curves. Acta Mathematica, 214(2), 357-393 - http://dx.doi.org/10.1007/s11511-015-0127-8
- Poineau, J., & Pulita, A. (2014). The convergence Newton polygon of a $p$-adic differential equation IV : local and global index theorems - https://arxiv.org/abs/1309.3940
- Poineau, J., & Pulita, A. (2013). The convergence Newton polygon of a $p$-adic differential equation III : global decomposition and controlling graphs - https://arxiv.org/abs/1308.0859
- Pulita, A. (2015). The convergence Newton polygon of a $p$-adic differential equation. I: Affinoid domains of the Berkovich affine line. Acta Mathematica, 214(2), 307-355 - http://dx.doi.org/10.1007/s11511-015-0126-9
