MAXIMUM NUMBER OF RATIONAL POINTS ON HYPERSURFACES IN WEIGHTED PROJECTIVE SPACES OVER FINITE FIELDS

Yves Aubry (1, 2, 3) , Marc Perret (4, 5)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 I2M - Institut de Mathématiques de Marseille
3 UTLN - Université de Toulon
4 IMT - Institut de Mathématiques de Toulouse UMR5219
5 UT2J - Université Toulouse - Jean Jaurès

An upper bound for the maximum number of rational points on an hypersurface in a projective space over a finite field has been conjectured by Tsfasman and proved by Serre in 1989. The analogue question for hypersurfaces on weighted projective spaces has been considered by Castryck, Ghorpade, Lachaud, O'Sullivan, Ram and the first author in 2017. A conjecture has been proposed there and proved in the particular case of the dimension 2. We prove here the conjecture in any dimension provided the second weight is also equal to one.

Mots clés: February 9; 2024 2010 Mathematics Subject Classification Primary 14G05; Secondary 14G15; 2024; 2010 Mathematics Subject Classification; Primary 14G05

Domaines: Géométrie algébrique [math.AG]

Yves Aubry, Marc Perret. MAXIMUM NUMBER OF RATIONAL POINTS ON HYPERSURFACES IN WEIGHTED PROJECTIVE SPACES OVER FINITE FIELDS. 2024. ⟨hal-04449392⟩