Chow groups and higher congruences for the number of rational points on proper varieties over finite fields
| dc.creator | Fakhruddin, Najmuddin | |
| dc.date | 2005-01-12 | |
| dc.date | 2006-03-30 | |
| dc.date.accessioned | 2026-07-07T06:39:16Z | |
| dc.date.available | 2026-07-07T06:39:16Z | |
| dc.description | Given a proper family of varieties over a smooth base, with smooth total space and general fibre, all over a finite field k with q elements, we show that a finiteness hypothesis on the Chow groups, CH_i, i=0,1,...,r, of the fibres in the family leads to congruences mod q^{r+1} for the number of rational points in all the fibres over k-rational points of the base. These hypotheses on the Chow groups are expected to hold for families of low degree intersections in many Fano varieties leading to a broad generalisation of the theorem of Ax--Katz, as well as results of the author and C. S. Rajan. As an unconditional application, we give an asymptotic generalisation of the Ax--Katz theorem to low degree intersections in a large class of homogenous spaces. | |
| dc.description | Added a section containing applications to low degree intersections in homogenous spaces | |
| dc.identifier | https://arxiv.org/abs/math/0501181 | |
| dc.identifier | http://arxiv.org/abs/math/0501181 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101016 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Chow groups and higher congruences for the number of rational points on proper varieties over finite fields | |
| dc.type | text |