发帖
雷达卡
摘要翻译：
给定一个定义在有限域上的射影簇X，因子的zeta函数试图计算X的所有不可约的余维子簇，每个子簇由它们的射影度来度量。当X的维数大于1时，这是一个纯p-adic函数，收敛于开放的单位圆盘上。有四个猜想成立，第一个猜想是对C_p全部的p-adic亚纯延拓。当X的因子类群（模线性等价因子）秩为1，则四个猜想均为真。本文讨论了高阶情形。特别地，我们证明了一个适用于大类变体的p-adic亚纯延拓定理。这类变体的例子是定义在有限域上的射影非奇异曲面（其有效么半群是有限生成的）和所有的射影多曲面变体（光滑的或奇异的）。
---
英文标题：
《On the zeta function of divisors for projective varieties with higher
rank divisor class group》
---
作者：
C. Douglas Haessig
---
最新提交年份：
2008
---
分类信息：
一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
--
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
---
英文摘要：
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).
---
PDF链接：
https://arxiv.org/pdf/0803.3355
京公网安备 11010802022788号
