摘要翻译：
证明了在M.Rost意义下具有特殊对应关系的类的函数域保持小余维数圈的合理性。Vishik在二次曲面中证明了这一事实，并在他构造具有$u$-不变的$2^r+1$的域中发挥了关键作用。主要的技术工具是Levine-Morel的代数协边性、广义Rost度公式和某些Landweber-Novikov运算的Chow迹的整除性。作为我们方法的直接应用，我们证明了所有$F_4$-变体的Vishik定理。
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英文标题：
《Special correspondences and Chow traces of Landweber-Novikov operations》
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作者：
Kirill Zainoulline
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  We prove that the function field of a variety which possesses a special correspondence in the sense of M. Rost preserves the rationality of cycles of small codimensions. This fact was proven by Vishik in the case of quadrics and played the crucial role in his construction of fields with $u$-invariant $2^r+1$. The main technical tools are algebraic cobordism of Levine-Morel, generalized Rost degree formula and divisibility of Chow traces of certain Landweber-Novikov operations. As a direct application of our methods we prove the Vishik's Theorem for all $F_4$-varieties.
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PDF链接：
https://arxiv.org/pdf/0708.3747