Fields medallists - 2018

Collection Fields medallists - 2018

00:00:00 / 00:00:00

19 26

The Witt vector affine Grassmannian

By Peter Scholze

Also appears in collections : Arithmetic geometry, representation theory and applications / Géométrie arithmétique, théorie des représentations et applications, The Fields Medallists

(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.

Information about the video

Date of recording 26/06/2015
Date of publication 09/07/2015
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent, Pascal Vichi
Format MP4

Citation data

DOI 10.24350/CIRM.V.18774403
Cite this video SCHOLZE, Peter (26/06/2015). The Witt vector affine Grassmannian. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18774403
URL https://dx.doi.org/10.24350/CIRM.V.18774403

Domain(s)

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. <arXiv:1307.3763> - http://arxiv.org/abs/1307.3763
[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. <arXiv:1407.8519> - http://arxiv.org/abs/1407.8519

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