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Post-edited An overview on some recent results about $p$-adic differential equations over Berkovich curves

Auteurs : Pulita, Andrea (Auteur de la Conférence)
CIRM (Editeur )

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Berkovich curves p-adic differential equations radius of convergence convergence Newton polygon controlling graph decomposition by the radii index theorem de Rham cohomology questions of the audience

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

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 06/04/17
    Date de captation : 28/03/17
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Domaine : Algebraic & Complex Geometry ; PDE
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2017-03-28_Pulita.mp4

Informations sur la rencontre

Nom du congrès : $p$-adic analytic geometry and differential equations / Géométrie analytique et équations différentielles $p$-adiques
Organisteurs Congrès : Lebacque, Philippe ; Nicaise, Johannes ; Poineau, Jérôme
Dates : 27/03/17 - 31/03/17
Année de la rencontre : 2017
URL Congrès : http://scientific-events.weebly.com/1609.html

Citation Data

DOI : 10.24350/CIRM.V.19153403
Cite this video as: 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

Bibliographie

  1. 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

  2. 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

  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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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



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