generalized cohomology and classifying spases
generalized cohomology and classifying spases
批准号:
15540004
负责人:
YAGITA Nobuaki
金额:
$1.02万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2003
资助国家:
日本
项目状态:
已结题
起止时间:
2003 至 2004
中文摘要
设p是素数,k是复数域C的子域,其中包含1的本原p次根。对k上有限型方案X,Suslin-Voevodsky([Su-Vo],[Vo2])构造了运动上同调H ^<*,*>(X; Z/p)=[symmetry]_<m,n> H ^<*,*>(X; Z/p).对光滑的X,上同调H ^<2 *,*>(X; Z/p)=[对称性]_nH ^<2n,n>(X; Z/p)与X上代数圈的经典模p Chow环CH ^*(X)/p相同.包含t_C:k <$C诱导了一个自然变换(实现映射)t ^<m,n>_C:H ^<m,n> → H ^m(X(C); Z/p)其中X(C)是C值点的复簇。记为(1.1)h ^<*,*>(X; Z/p)=[symmetry]_<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),其中t ^*_C(r)= 1。然后我们有双阶代数单态(1.2)h ^<*,*>(XZ/p)<$H ^*(X(C); Z/p)[叉积] Z/p [r,r ^]其中x ∈ H ^n(X(C); Z/p)的双阶由(n,n)给出。<-1>当k C和Beilinson-Lichtenbaum猜想对p成立时,我们也有注入II ^*(X; Z/p)[叉积] Z/p [r]<$h ^<*,*>(X; Z/p).其中t ^<m,n>_C:H ^<m,n>(X; Z/p)→ H ^m(X(C); Z/p)是X到C值点X(C)的实现映射。假设k = C,并且B(m,p)条件成立。则这个双阶代数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同构为gr H ^*(X(C); Z/p)[叉积] Z/p [r]的双度模,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:
DOI:
--
发表时间:
2004
期刊:
J.Kyoto Math. 44
影响因子:
--
作者:
[N.Yagita]
通讯作者:
N.Yagita
共 16 条
algebraic cobordism and motivic cohomology
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批准号:20540061
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.75万
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财政年份:2008
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负责人:YAGITA Nobuaki
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依托单位:
motivic cohomology and classifying spaces
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批准号:17540007
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$1.63万
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财政年份:2005
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负责人:YAGITA Nobuaki
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依托单位:
Cohomology of groups and BP-theory
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批准号:10640059
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$0.83万
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财政年份:1998
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负责人:YAGITA Nobuaki
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依托单位:
海外基金