60,842 research outputs found
Meromorphy of the rank one unit root L-function revisited
We demonstrate that Wan's alternate description of Dwork's unit root
L-function in the rank one case may be modified to give a proof of meromorphy
that is classical, eliminating the need to study sequences of uniform
meromorphic functions.Comment: 9 page
On the zeta function of divisors for projective varieties with higher rank divisor class group
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).Comment: Significant Improvements. 13 page
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