The Grothendieck duality theorem via Bousfield’s techniques and Brown representability
The Grothendieck duality theorem via Bousfield’s techniques and Brown representability
复制标题
DOI：
10.1090/s0894-0347-96-00174-9
复制
发表时间：
1996
影响因子：
3.9
通讯作者：
A. Neeman
中科院分区：
文献类型：
--
作者：
A. Neeman
Grothendieck 证明，如果 f: X ) Y 是好方案的真态射，则 Rf* 具有右伴随，它以与相对规范丛的张量积形式给出。最初的证明是通过修补本地数据。 Deligne 通过全局论证证明了伴随性的存在性，Verdier 证明了该全局伴随性可以在局部计算。在本文中，我们证明伴随的存在是布朗可表征定理的直接结果。通过“粉碎”论证，几乎可以立即得出，伴随物是由具有对偶复形的张量积给出的。 Verdier 的基变定理是一个简单的推论。弗吉尼亚大学数学系，夏洛特维尔，弗吉尼亚州 22903 电子邮件地址：an3rQvirginia。 edu 此内容于 2016 年 9 月 7 日星期三 06:26:19 UTC 从 157.55.39.27 下载 所有使用均受 http://about.jstor.org/terms 约束
Grothendieck proved that if f: X ) Y is a proper morphism of nice schemes, then Rf* has a right adjoint, which is given as tensor product with the relative canonical bundle. The original proof was by patching local data. Deligne proved the existence of the adjoint by a global argument, and Verdier showed that this global adjoint may be computed locally. In this article we show that the existence of the adjoint is an immediate consequence of Brown's representability theorem. lIt follows almost as imme- diately, by "smashing" arguments, that the adjoint is given by tensor product with a dualising complex. Verdier's base change theorem is an easy conse- quence. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF VIRGINIA, CHARLOTTESVILLE, VIRGINIA 22903 E-mail address: an3rQvirginia. edu This content downloaded from 157.55.39.27 on Wed, 07 Sep 2016 06:26:19 UTC All use subject to http://about.jstor.org/terms