Loading...
Loading...

Go to the content (press return)

Del Pezzo surfaces over finite fields and their Frobenius traces

Author
Banwait, B.; Fite, F.; Loughran, D.
Type of activity
Journal article
Journal
Mathematical proceedings of the Cambridge Philosophical Society
Date of publication
2019-07
Volume
167
Number
1
First page
35
Last page
60
DOI
https://doi.org/10.1017/S0305004118000166 Open in new window
Repository
http://hdl.handle.net/2117/124690 Open in new window
URL
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/del-pezzo-surfaces-over-finite-fields-and-their-frobenius-traces/3D70794B5F27B0D655F34987CB2EB6F4 Open in new window
Abstract
Let S be a smooth cubic surface over a finite field q. It is known that #S( q) = 1 + aq + q2 for some a ¿ {-2, -1, 0, 1, 2, 3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special cases treated by Swinnerton–Dyer, we give a complete answer to this question. We also answer the analogous question for other del Pezzo surfaces, and consider the inverse Galois problem for del Pezzo surfaces over finite fields. Finally we give a corrected version of Manin's and ...
Citation
Banwait, B., Fite, F., Loughran, D. Del Pezzo surfaces over finite fields and their Frobenius traces. "Mathematical proceedings of the Cambridge Philosophical Society", July 2019, vol. 167, núm. 1, p. 35-60.
Group of research
TN - Number Theory Research Group

Participants

  • Banwait, Barinder  (author)
  • Fite Naya, Francesc  (author)
  • Loughran, Daniel  (author)

Attachments