| Original language | English |
|---|---|
| Pages (from-to) | 1-57 |
| Number of pages | 57 |
| Journal | Acta Mathematica |
| Volume | 221 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Funding Information:The first author was partially supported by the NSF grants DMS-1102434 and DMS-1601953. The second and third authors acknowledge the support of EPSRC grant EP/H018891/1. The third author acknowledges the support of ERC advanced grant 247034, ISF grants 1117/13 and 686/17, BSF grant 2016072 and the Vinik chair of mathematics which he holds. The fourth author was partially supported by the NSF grants DMS-1839351 and DMS-1840702, the Simons Foundation Fellowship 305247, the EPSRC, and the Mathematisches Forschungsinstitut Oberwolfach.Parts of the paper were written while the fourth author visited the Departments of Mathematics of Imperial College, London, and University of Chicago. It is a pleasure to thank Imperial College, Prof. Ngo Bao Chau, and the University of Chicago for generous hospitality and stimulating environment. The authors also thank M. Geck, G. Malle, J. Michel, and especially J. Taylor for many helpful discussions. The authors are grateful to the referees for careful reading and helpful comments on the paper.
Funding Information:
The first author was partially supported by the NSF grants DMS-1102434 and DMS-1601953. The second and third authors acknowledge the support of EPSRC grant EP/H018891/1. The third author acknowledges the support of ERC advanced grant 247034, ISF grants 1117/13 and 686/17, BSF grant 2016072 and the Vinik chair of mathematics which he holds. The fourth author was partially supported by the NSF grants DMS-1839351 and DMS-1840702, the Simons Foundation Fellowship 305247, the EPSRC, and the Mathematisches Forschungsinstitut Oberwolfach.