论文标题
Steenrod操作和代数类
Steenrod operations and algebraic classes
论文作者
论文摘要
基于odale同谋的相对WU定理，我们研究了Chow组和étale共同体的Steenrod操作的兼容性。利用由代数的结果障碍，我们在各个字段上构建了非代数共同体学课程的新示例（$ \ Mathbb {c} $，$ \ Mathbb {r} $，$ \ overline {\ Mathbb {F}} _ p $，$ \ p $，$ \ Mathbb {f} $ ____________________________________________________________ 我们还使用steenrod操作来研究紧凑型$ \ MATHCAL {C}^{\ infty} $歧管$ M $的Mod 2 $共同体类别，这些$ M $是可代数的，即在某些$ M $的真实代数模型上代数。我们给出了代数和非代数的课程的新示例，回答了Benedetti，Dedò和Kucharz的问题。
Based on a relative Wu theorem in étale cohomology, we study the compatibility of Steenrod operations on Chow groups and on étale cohomology. Using the resulting obstructions to algebraicity, we construct new examples of non-algebraic cohomology classes over various fields ($\mathbb{C}$, $\mathbb{R}$, $\overline{\mathbb{F}}_p$, $\mathbb{F}_q$). We also use Steenrod operations to study the mod $2$ cohomology classes of a compact $\mathcal{C}^{\infty}$ manifold $M$ that are algebraizable, i.e. algebraic on some real algebraic model of $M$. We give new examples of algebraizable and non-algebraizable classes, answering questions of Benedetti, Dedò and Kucharz.
