论文标题
残留场上的双磷仪说明：GALOIS分层和均匀性
Diophantine statements over Residue fields: Galois stratification and uniformity
论文作者
论文摘要
使用Felgner的问题，我在使用[FRS76]中首次出现的“ GALOIS分层程序”时重新审视了一个关键问题。这里的重点是使用算术同型来制造庞美列的生产。连接到一般性毒液陈述的串联规范。 根据Michael Benedikt和E. hrushovski的进行工作，Galois分层 - 在一个有限场上 - 尽可能有效：在长度N的陈述上，它需要由n中线性长度的指数的堆叠来限制的。这并不能利用使用同质副本方面，CHOW动机有效的问题，就像我的主要示例中有关特殊封面的概括所带来的。 该示例[FRJ，第一章。 30]，简化了原始过程的各个方面。它将其与后来的Frobenius字段理论相结合，以在Q上产生对象，其减少mod Primes给出了分层程序。该纸分离了Chebotarev非规范类似物的两种不同用途。 1。直接从Chow Motives的痕迹中解释庞加罗系列系数的田间交叉（提供有关Prime P的变化的有价值的陈述； 2. Chebotarev使用lang-weil近似适当品种的Galois分层程序的点数。 我们考虑在z/p的代数关闭中采用值的变量，但通过弗罗贝尼乌斯的各个力量固定：我们称这些frobenius载体。为此，有一个扭曲的Chebotarev版本，源于deligne的猜想，并在Hrushovski的预印本中概述。本文扩展了D. Wan，J。Denef和F. Loeser，J。Nicaise，I。Tomasic和E. Hrushovski的工作，所有这些都与将Galois分层程序相关的是超越原始有限的现场框架。
Using Felgner's problem I revisit a key issue in using the "Galois Stratification Procedure" that first appeared in [FrS76]. The emphasis here is on using arithmetic homotopy to make the production of Poincare; series attached to general diophantine statements canonical. According to work in progress of Michael Benedikt and E. Hrushovski, Galois stratification - over one finite field - is as efficient as is possible: on a statement of length n, it requires time bounded by a stack of exponentials of length linear in n. This doesn't take advantage of problems prepped for using homotopy aspects, Chow Motives, efficiently as in the main example which comes from my paper on the generalization of exceptional covers. That example [FrJ, Chap. 30], simplifies aspects of the original procedure. It combines this with the later theory of Frobenius fields to produce objects over Q whose reductions mod primes give the stratification procedure at the prime. The paper separates two different uses of the Chebotarev non-regular analog. 1. Field crossing to interpret Poincare series coefficients directly from traces on Chow motives (providing valuable statements on variation with the prime p; versus 2. Chebotarev using Lang-Weil to approximate the number of points on an appropriate variety for the Galois stratification procedure. We consider variables taking values in the algebraic closure of Z/p but fixed by respective powers of the Frobenius: we call these Frobenius vectors. For this there is a twisted Chebotarev version stemming from a conjecture of Deligne, and outlined in a preprint of Hrushovski. This paper expands on the work of D. Wan, J. Denef and F. Loeser, J. Nicaise, I. Tomasic and E. Hrushovski, all relevant to taking the Galois stratification procedure beyond the original finite field framework.
