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Arithmetic $D$-modules and existence of crystalline companion

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Authors : Abe, Tomoyuki (Author of the conference)
CIRM (Publisher )

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Abstract : We will show that there exists a correspondence between smooth $l$-adic sheaves and overconvergent $F$-isocrystals over a curve preserving the Frobenius eigenvalues. Moreover, we show the existence of $l$-adic companions associated to overconvergent $F$-isocrystals for smooth varieties.
Some part of the work is done jointly with Esnault.

MSC Codes :
12H25 - $p$-adic differential equations
14F10 - Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14F30 - $p$-adic cohomology, crystalline cohomology

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 06/04/17
    Conference Date : 29/03/17
    Subseries : Research talks
    arXiv category : Algebraic Geometry ; Number Theory
    Mathematical Area(s) : Algebraic & Complex Geometry
    Format : MP4 (.mp4) - HD
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2017-03-29_Abe.mp4

Information on the Event

Event Title : $p$-adic analytic geometry and differential equations / Géométrie analytique et équations différentielles $p$-adiques
Event Organizers : Lebacque, Philippe ; Nicaise, Johannes ; Poineau, Jérôme
Dates : 27/03/17 - 31/03/17
Event Year : 2017
Event URL : http://conferences.cirm-math.fr/1609.html

Citation Data

DOI : 10.24350/CIRM.V.19154103
Cite this video as: Abe, Tomoyuki (2017). Arithmetic $D$-modules and existence of crystalline companion. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19154103
URI : http://dx.doi.org/10.24350/CIRM.V.19154103

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