Number of points of Deligne-Lusztig surfaces
This paper contains detailed proofs of results previously announced by the author [C. R. Acad. Sci., Paris, Sér. I 322, 563-566 (1996; Zbl 0918.11034)]. The author determines the zeta functions and Betti numbers for smooth compactifications of Deligne-Lusztig surfaces associated to various connected, reductive algebraic groups over an algebraic closure of a finite field \({\mathbb F}_q\). In most of the examples, the number of rational points over \({\mathbb F}_q\) or over \({\mathbb F}_{q^2}\) attains the bound of Weil-Deligne. The author also shows that the surfaces associated to groups of type \({}^2A_4\) are minimal surfaces of general type.
scientific article; zbMATH DE number 1471039
scientific article