Geodesic
Rigidity of spreadings and fields of definition
Chris Peters1
1TU Eindhoven, Netherlands
EMS surveys in mathematical sciences, Tome 4 (2017) no. 1, pp. 77-100

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DOI

Varieties without deformations are defined over a number field. Several old and new examples of this phenomenon are discussed such as Bely ̆ı curves and Shimura varieties. Rigidity is related to maximal Higgs fields which come from variations of Hodge structure. Basic properties for these due to P. Griffiths, W. Schmid, C. Simpson and, on the arithmetic side, to Y. André and I. Satake all play a role. This note tries to give a largely self-contained exposition of these manifold ideas and techniques, presenting, where possible, short new proofs for key results.
DOI : 10.4171/emss/4-1-4
Classification : 14-XX, 11-XX
Mots-clés : Belyı curves, Beauville surfaces, fields of definition, Higgs fields, rigidity, Shimura varieties, spreads

Chris Peters  1

1 TU Eindhoven, Netherlands 
Chris Peters. Rigidity of spreadings and fields of definition. EMS surveys in mathematical sciences, Tome 4 (2017) no. 1, pp. 77-100. doi: 10.4171/emss/4-1-4
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