Baldi, G;
(2019)
Local to global principle for the moduli space of K3 surfaces.
Archiv der Mathematik
10.1007/s00013-018-01295-1.
(In press).
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Abstract
Recently S. Patrikis, J.F. Voloch, and Y. Zarhin have proven, assuming several well-known conjectures, that the finite descent obstruction holds on the moduli space of principally polarised abelian varieties. We show an analogous result for K3 surfaces, under some technical restrictions on the Picard rank. This is possible since abelian varieties and K3s are quite well described by ‘Hodge-theoretical’ results. In particular the theorem we present can be interpreted as follows: a family of ℓ -adic representations that looks like the one induced by the transcendental part of the ℓ -adic cohomology of a K3 surface (defined over a number field) determines a Hodge structure which in turn determines a K3 surface (which may be defined over a number field).
| Type: | Article |
|---|---|
| Title: | Local to global principle for the moduli space of K3 surfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00013-018-01295-1 |
| Publisher version: | https://doi.org/10.1007/s00013-018-01295-1 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10073516 |
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