Français
The Witt vector affine Grassmannian
Multi angle
Authors : Scholze, Peter (Author of the conference)
CIRM (Publisher )
14F30 - $p$-adic cohomology, crystalline cohomology
14G22 - Rigid analytic geometry
13F35 - Witt vectors and related rings
CIRM (Publisher )
Loading the player...
|
Abstract :
(joint with Bhargav Bhatt) We prove that the space of $W(k)$-lattices in $W(k)[1/p]^n$, for a perfect field $k$ of characteristic $p$, has a natural structure as an ind-(perfect scheme). This improves on recent results of Zhu by constructing a natural ample line bundle on the space of such lattices.
MSC Codes : 14F30 - $p$-adic cohomology, crystalline cohomology
14G22 - Rigid analytic geometry
13F35 - Witt vectors and related rings
|
Information on the Video
Film maker : Vichi, Pascal ; Hennenfent, GuillaumeLanguage : English Available date : 09/07/15 Conference Date : 26/06/15 Series : The Fields Medallists Subseries : Research talks arXiv category : Algebraic Geometry ; Number Theory Mathematical Area(s) : Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:02:18 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-06-26_Scholze.mp4 
|
Information on the Event
Event Title : Arithmetic geometry, representation theory and applications / Géométrie arithmétique, théorie des représentations et applicationsEvent Organizers : Abbes, Ahmed ; Breuil, Christophe ; Chenevier, Gaëtan ; Saito, Takeshi Dates : 22/06/15 - 26/06/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1185.html
Citation Data
DOI : 10.24350/CIRM.V.18774403Cite this video as: Scholze, Peter (2015). The Witt vector affine Grassmannian. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18774403 URI : http://dx.doi.org/10.24350/CIRM.V.18774403 |
Bibliography
- [1] Beauville, A., & Laszlo, Y. (1994). Conformal blocks and generalized theta functions. Communications in Mathematical Physics, 164(2), 385-419 - http://dx.doi.org/10.1007/BF02101707
- [2] Bhatt, B., & Scholze, P. Projectivity of the Witt vector affine Grassmannian, preprint -
- [3] Bhatt, B., Schwede, K., & Takagi, S. (2014). The weak ordinarity conjecture and F-singularities.
- [4] Kreidl, M. (2014). On $p$-adic lattices and Grassmannians. Mathematische Zeitschrift, 276(3-4), 859-888 - http://dx.doi.org/10.1007/s00209-013-1225-y
- [5] Zhu, X. (2014). Affine Grassmannians and the geometric Satake in mixed characteristic.
