绝对伽罗瓦群忠实地作用于 一般型曲面的模空间

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

摘要翻译：
我们证明了Galois群$Gal(\bar{\q}/\q)$忠实于一般型曲面模空间的连通分量集，并证明了对于Gal(\bar{\q}/\q)$中与恒等式和复共轭不同的每个元素$\sigma，存在一个一般型曲面，使得$x$和Galois共轭簇$x^{\sigma}$具有非同构的基本群。该结果由第二作者在2006年9月的Alghero会议“代数变体的拓扑”上宣布。在本文写作之前，我们收到了Robert Easton和Ravi Vakil的一个非常有趣的预印本(\cite{e-v}），其中用完全不同类型的例子证明了Galois群$gal(\bar{\q}/\q)$忠实于一般型曲面模空间的不可约分量集。我们还给出了具有Galois共轭的非同构基本群的曲面的其他更简单的例子，从而具有同构的代数基本群。
---
英文标题：
《The absolute Galois group acts faithfully on the connected components of
  the moduli space of surfaces of general type》
---
作者：
Ingrid Bauer and Fabrizio Catanese (Universitaet Bayreuth), Fritz
  Grunewald (Universitaet Duesseldorf)
---
最新提交年份：
2007
---
分类信息：

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
--
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
--

---
英文摘要：
  We show that the Galois group $Gal(\bar{\Q} /\Q)$ operates faithfully on the set of connected components of the moduli spaces of surfaces of general type, and also that for each element $\sigma \in Gal(\bar{\Q} /\Q)$ different from the identity and from complex conjugation, there is a surface of general type such that $X$ and the Galois conjugate variety $X^{\sigma}$ have nonisomorphic fundamental groups. The result was announced by the second author at the Alghero Conference 'Topology of algebraic varieties' in september 2006. Before the present paper was actually written, we received a very interesting preprint by Robert Easton and Ravi Vakil (\cite{e-v}), where it is proven, with a completely different type of examples, that the Galois group $Gal(\bar{\Q} /\Q)$ operates faithfully on the set of irreducible components of the moduli spaces of surfaces of general type. We also give other simpler examples of surfaces with nonisomorphic fundamental groups which are Galois conjugate, hence have isomorphic algebraic fundamental groups.
---
PDF链接：
https://arxiv.org/pdf/0706.1466

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：Fundamental mathematics interesting Fundamenta Components 变体 给出 fundamental 曲面 收到