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The non-positive equivariant stems.

机译:非正等变茎。

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摘要

Part I. The G-equivariant analogues of the stable homotopy groups of spheres are the equivariant homotopy groups of stable homotopy representations. Let G be a compact Lie group and A(G) the Burnside ring of G. Let Z be a stable homotopy representation with non-negative dimension function. We prove, with one extra hypothesis on Z, that pG0 (Z), as an A(G)-module, is isomorphic to a quotient of A(G) tensored with an invertible A(G)-module. This is the equivariant analogue of the non-positive stems.; Part II. We investigate the Picard group Pic( DM ) of isomorphism classes of invertible objects in the derived category of O -modules for a commutative unital ringed Grothendieck topos ( E,O ) with enough points. Let C(pt( E )) denote the additive group of continuous functions from the space of isomorphism classes of points of E to the integers. When the ring O p has connected prime ideal spectrum for all points p of E we show that Pic( DM ) is naturally isomorphic to the Cartesian product of C(pt( E )) with the Picard group of O -modules Also, for a commutative unital ring R, the group Pic( D R) is isomorphic to the Cartesian product of Pic(R) and the additive group of continuous functions from spec R to the integers.
机译:第一部分,球的稳定同构基团的G等价类似物是稳定同构表示的等变同构基团。假设G是一个紧凑的Lie基团,而A(G)是G的Burnside环。假设Z是一个具有非负维数函数的稳定同伦表示。我们用Z的另一种假设证明,pG0(Z)作为A(G)-模,是同构于可逆A(G)-模张量的A(G)的商。这是非阳性茎的等变类似物。第二部分我们研究了具有足够点的可交换单元环格洛腾迪克题库(E,O)的O模块派生类别中可逆对象的同构类的Picard群Pic(DM)。令C(pt(E))表示从E点的同构类空间到整数的连续函数的加法组。当环O p已连接E的所有点p的本征理想谱时,我们证明Pic(DM)与带有O-模块的Picard组的C(pt(E))的笛卡尔积自然同构。在交换单环R上,基团Pic(DR)与Pic(R)的笛卡尔积同构,并且是从spec R到整数的连续函数的加法组。

著录项

  • 作者

    Fausk, Halvard.;

  • 作者单位

    The University of Chicago.;

  • 授予单位 The University of Chicago.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2001
  • 页码 44 p.
  • 总页数 44
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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