motivic cohomology and classifying spaces

动机上同调和分类空间

• 批准号: 17540007
• 负责人: YAGITA Nobuaki
• 金额: $ 1.63万
• 依托单位: Ibaraki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540007/
• 关键词: motvic cohomology; classifying space; BP-theory; motivic cohomology; algebraic cobordism; Pfister quadric; コンプレックスコボルディズム; 代数的コボルディズム

A Suslin and V. Voevodsky constructed and developed the motivic cohomology theory H^{*, *''} (X; Z/p) for algebraic sets X over the base field k. This theory is the counter part in algebraic geometry of the usual mod p singular cohomology in algebraic topology. Let ch (k)=0 and fix an embedding that k is subset C. As the counter part of the complex cobordism theory MU^* (X), Voevodsky defined the algebraic cobordism theory MGL^{*, *''} (X) and used it in the first proof of the Milnor Conjecture. Given a nonzero symbol a in K_{n+1}^M (k)/p, the norm variety V_a is a variety such that a=0 in K_{n+1}^M (k (V_a))/p and V_a c=v_n. Here v_n is the 2 (p^n-1) complex manifold generating the coefficient ring of the BP-theory in algebraic topology. In these papers we write down the properties of ABP^{*, *''} (X) which is the algebraic counter part of BP-theory. For example we give a construction of the Atiyah-Hirzebruch spectral sequence for ABP^{*, *} (X; \bZ/p); its existence (of$MGL$-version) was announced by Hopkins and Morel more that several years before, however any proof (or even statement), does not appear yet. We study the cohomology operations, products and Gysin maps explicitly in $ABP^{*, *''}$-theory.

A Suslin和V.Voevodsky构造和发展了基域k上代数集合X的Motivic上同调理论H^{*，*‘’}(X；Z/p)，该理论是代数几何中通常的mod p奇异上同调的对立面.设ch(K)=0，固定嵌入k是子集C，作为复余边理论MU^*(X)的对应部分，Voevodsky定义了代数余边理论Mgl^{*，*‘’}(X)，并将其用于Milnor猜想的第一个证明.给定K_(n+1)^M(K)/p中的一个非零符号a，范数簇V_a是使得在K_(n+1)^M(k(V_A))/p中a=0且V_ac=v_n的簇.这里v_n是生成代数拓扑学中BP理论的系数环的2(p^n-1)复流形.在这些文章中，我们记录了BP理论的代数对应部分ABP^{*，*‘’}(X)的性质。例如，我们给出了ABP^{*，*}(X；\bz/p)的Atiyah-Hirzebruch谱序列的构造；它的存在($MGL$-版本)是由Hopkins和Morel More在几年前宣布的，然而任何证明(甚至是陈述)还没有出现。我们在$ABP^{*，*‘’}-理论中显式地研究了上同调运算、乘积和Gysin映射。

项目成果

A gap theorem for complete for-dimensional manifolds with ΔW_t=0

ΔW_t=0 的完整 for 维流形的间隙定理

• 发表时间: 2005
• 期刊: Tsukuba J.Math. 29
• 作者: Y.Hashimoto;M.kaneda;D.Rumjnin;N.Yagita;N.Yagita;N. Yagita;N. Yagita;N.Yagita;N.Yagita;N.Yagita;T.Okayasu
• 通讯作者: T.Okayasu

Algebraic cobordism of a Pfister form

Pfister 形式的代数共边

• 发表时间: 2007
• 期刊: J. London Math. Soc 76
• 作者: A.Vishik;N.Yagita;A. Vishik and N. Yagita
• 通讯作者: A. Vishik and N. Yagita

茨城大学研究者情報総覧

茨城大学研究员信息一览

Algebraic cobordism of compact Lie groups

紧李群的代数共边

• 发表时间: 2005
• 期刊: J. Proc Camb. Soc 139
• 作者: Y.Hashimoto;M.kaneda;D.Rumjnin;N.Yagita;N.Yagita;N. Yagita
• 通讯作者: N. Yagita

Applications of Atiyah-Hizebruch spectral sequences for motivic cobordism

Atiyah-Hizebruch 谱序列在动机共边中的应用

• 发表时间: 2005
• 期刊: Proc.London Math.Soc. 90
• 作者: Y.Hashimoto;M.kaneda;D.Rumjnin;N.Yagita;N.Yagita;N. Yagita;N. Yagita;N.Yagita;N.Yagita
• 通讯作者: N.Yagita