On the zeta function of divisors for projective varieties with higher rank divisor class group
| dc.creator | Haessig, C. Douglas | |
| dc.date | 2008-03-24 | |
| dc.date | 2008-08-04 | |
| dc.date.accessioned | 2026-07-07T09:54:09Z | |
| dc.date.available | 2026-07-07T09:54:09Z | |
| dc.description | Given a projective variety X defined over a finite field, the zeta function of divisors attempts to count all irreducible, codimension one subvarieties of X, each measured by their projective degree. When the dimension of X is greater than one, this is a purely p-adic function, convergent on the open unit disk. Four conjectures are expected to hold, the first of which is p-adic meromorphic continuation to all of C_p. When the divisor class group (divisors modulo linear equivalence) of X has rank one, then all four conjectures are known to be true. In this paper, we discuss the higher rank case. In particular, we prove a p-adic meromorphic continuation theorem which applies to a large class of varieties. Examples of such varieties are projective nonsingular surfaces defined over a finite field (whose effective monoid is finitely generated) and all projective toric varieties (smooth or singular). | |
| dc.description | Significant Improvements. 13 pages | |
| dc.identifier | https://arxiv.org/abs/0803.3355 | |
| dc.identifier | http://arxiv.org/abs/0803.3355 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166209 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | On the zeta function of divisors for projective varieties with higher rank divisor class group | |
| dc.type | text |