Some elementary theorems about algebraic cycles on abelian varieties
Some elementary theorems about algebraic cycles on abelian varieties
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关于阿贝尔簇代数循环的一些基本定理
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发表时间：
1976
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通讯作者：
S. Bloch
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作者：
S. Bloch
研究了代数闭域上n维阿贝尔变型a上0环模有理等价群的结构。这个群形成了庞特里亚金积下的增广的n -代数，其增广由度映射给出。增广理想i的(n+1)-st次幂（=0次循环）显示为零，而对于合适的k（例如k=复数）则幂i是非零的。作为推论，每个0度的0循环都被证明是合理地等价于因子的交点之和。部分结果证明了商si *r/I*r+1与协维数onA的循环之间的关系，类似于ena与Pic0A之间的等因性。
The structure of the group of 0-cycles modulo rational equivalence on ann-dimensional abelian varietyA over an algebraically closed fieldk is studied. This group forms an augmented ℤ-algebra under Pontryagin product, with augmentation given by the degree map. The (n+1)-st power of the augmentation idealI(=0-cycles of degree 0) is shown to be zero, while for suitablek (e.g.k=complex numbers) then-th power ofI is non-zero. As corollary, every 0-cycle of degree 0 is shown to be rationally equivalent to a sum of intersections of divisors. Partial results, analogous to the isogeny betweenA and Pic0A, are proved relating quotientsI*r/I*r+1 to cycles of codimensionr onA.