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generalized cohomology and classifying spases

generalized cohomology and classifying spases
广义上同调和空间分类
批准号:
15540004
负责人:
YAGITA Nobuaki
金额:
$1.02万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2003
资助国家:
日本
项目状态:
已结题
起止时间:
2003 至 2004

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中文摘要
翻译
设p是素数,k是复数域C的子域,复数域C包含1的本原p次根。对于k上有限类型的方案X,由Suslin-Voevodsky([SU-Vo],[Vo2])构造了模上同调H^<*,*>(X;Z/p)=[对称性]_<m,n>H^<*,*>(X;Z/p)。对于光滑X,上同调H^<2*,*>(X;Z/p)=[对称性]_nH^<2n,n>(X;Z/p)与X上经典的代数圈的mod p-Chow环CH^*(X)/p一致。包含t_C:K⊂C诱导一个自然变换(实现映射)t^<m,n>_C:H^<m,n>→H^m(X(C);Z/p),其中X(C)是C值点的复变。设(1.1)h^<*,*>(X;Z/p)=[对称性]_<m,n>H^<m,n>(X;Z/p)/Ker(t^<m,n>_C)已知存在元素r∈H^<0,1>(SPECK(K);Z/p),t^*_C(R)=1,则(1.2)h^<*,*>(Xz/p)〓H^*(X(C);Z/p)[叉积]Z/p[r,r^<-1>]其中x∈H^n(X(C);Z/p)的二次由(n,n)给出。当k C和Beilinson-Lichtenbaum猜想对p成立时,我们还有内射II^*(X;Z/p)[叉积]Z/p[r]〓h^<*,*>(X;Z/p)其中t^<m,n>_C:h^<m,n>(X;Z/p)→H^m(X(C);Z/p)是到X的C值点X(C)的实现映射。假设k=C且B(m,p)-条件成立。然后这个二次代数h^<*,*>(X;Z/p)通过滤子F_1=Im(t^<*,i>_C)和0≠r∈H^<0,1>(Spec(C);Z/p)〓Z/p同构于GR H^*(X(C);Z/p)[叉积]Z/p,但乘法不同。
英文摘要
Let p be a prime number and k a subfield of the complex number field C, which contains a primitive p-th root of 1. For a scheme X of finite type over k, the motivic cohomology H^<*,*> (X ; Z/p) = 【symmetry】_<m,n>H^<*,*> (X ; Z/p) is constructed by Suslin-Voevodsky ([Su-Vo],[Vo2]). For a smooth X, the cohomology H^<2*,*> (X ; Z/p) = 【symmetry】_nH^<2n,n> (X ; Z/p) is identified with CH^* (X)/p the classical mod p Chow ring of algebraic cyles on X.The inclusion t_C : k ⊂ C induces a natural transformation (realization map) t^<m,n>_C : H^<m,n> → H^m(X(C) ; Z/p) where X(C) is the complex variety of C-valued points. Let us write the coimage(1.1)h^<*,*>(X ; Z/p) = 【symmetry】_<m,n>H^<m,n>(X ; Z/p)/Ker(t^<m,n>_C)It is known that there is an element r ∈ H^<0,1>(Speck(k) ; Z/p) with t^*_C(r) = 1. Then we have the bigraded algebra monomorphism(1.2)h^<*,*>(XZ/p) 〓 H^* (X(C) ; Z/p)【cross product】Z/p[r,r^<-1>]where the bidegree of x ∈ H^n (X(C) ; Z/p) is given by (n,n). When k C and the Beilinson-Lichtenbaum conjecture is true for p, we also have the injection II^*(X ; Z/p)【cross product】Z/p[r] 〓 h^<*,*>(X ; Z/p).where t^<m,n>_C : H^<m,n>(X ; Z/p) → H^m(X(C) ; Z/p) is the realization map to C-valued points X(C) of X. Suppose that k = C and the B(m,p)-condition holds. Then this bigraded algebra h^<*,*> (X ; Z/p) is isomorphic as bidegree modules to gr H^*(X(C) ; Z/p)【cross product】Z/p[r] by the filtration F_1 = Im(t^<*,i>_C) and 0 ≠ r ∈ H^<0,1>(Spec(C) ; Z/p) 〓 Z/p, while the multiplications are different.
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Examples for mod p motivic cohomology of classifying
分类的 mod p 动机上同调示例
DOI: --
发表时间: 2003
期刊: Trans.Amer.Math.Soc. 355
影响因子: --
作者: [N.Yagita, M.Kaneda, Y.Kamiyama, N.Yagita]
通讯作者: N.Yagita
On certain maximal cycle modules for the special linier algebra at a root of units
关于单位根处特殊线性代数的某些最大循环模
DOI: --
发表时间: 2003
期刊: Pacific J.Math. 211
影响因子: --
作者: [N.Yagita, M.Kaneda, Y.Kamiyama, N.Yagita, M.Kaneda]
通讯作者: M.Kaneda
Example for the mod p motivic cohomology of classifying spaces.
分类空间的 mod p 动机上同调示例。
DOI: --
发表时间: 2003
期刊: Trans.AMS 355
影响因子: --
作者: [N.Yagita, M.Kaneda, Y.Kamiyama, N.Yagita, M.Kaneda, N.Yagita]
通讯作者: N.Yagita
Nobuaki Yagita: "Example for the mod P motivic cohomology of classifying spaces"Transactions Amer.Math.Soc.. 355. 4427-4450 (2003)
Nobuaki Yagita:“分类空间的 mod P 动机上同调的示例”Transactions Amer.Math.Soc.. 355. 4427-4450 (2003)
DOI: --
发表时间:
期刊:
影响因子: --
作者: []
通讯作者:
共 16 条
    algebraic cobordism and motivic cohomology
    • 批准号:
      20540061
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.75万
    • 财政年份:
      2008
    • 负责人:
      YAGITA Nobuaki
    • 依托单位:
    motivic cohomology and classifying spaces
    • 批准号:
      17540007
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $1.63万
    • 财政年份:
      2005
    • 负责人:
      YAGITA Nobuaki
    • 依托单位:
    Cohomology of groups and BP-theory
    • 批准号:
      10640059
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $0.83万
    • 财政年份:
      1998
    • 负责人:
      YAGITA Nobuaki
    • 依托单位:
    海外基金