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Codimension 2 cycles on Severi–Brauer varieties and decomposability
manuscripta mathematica ( IF 0.5 ) Pub Date : 2020-07-23 , DOI: 10.1007/s00229-020-01232-z
Eoin Mackall

In this text we show that one can generalize results showing that $$\mathrm {CH}^2(X)$$ , for various Severi–Brauer varieties X, is sometimes torsion free. In particular we show that for any pair of odd integers (n, m), with m dividing n and sharing the same prime factors, one can find a central simple k-algebra A of index n and exponent m that moreover has $$\mathrm {CH}^2(X)$$ torsion free for $$X=\mathrm {SB}(A)$$ . One can even take $$k={\mathbb {Q}}$$ in this construction.

中文翻译:

Severi-Brauer 变体和可分解性的 Codimension 2 循环

在本文中,我们展示了可以概括结果,表明 $$\mathrm {CH}^2(X)$$ ,对于各种 Severi-Brauer 变体 X,有时是无扭转的。特别地,我们证明了对于任何一对奇数 (n, m),其中 m 除以 n 并共享相同的质因数,人们可以找到索引为 n 和指数为 m 的中心简单 k 代数 A,而且它具有 $$\ mathrm {CH}^2(X)$$ 对于 $$X=\mathrm {SB}(A)$$ 无扭转。在这种构造中,甚至可以采用 $$k={\mathbb {Q}}$$。
更新日期:2020-07-23
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