Cohomology Operations
Cohomology Operations
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DOI：
10.2307/j.ctv941tx2.18
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
Christian Haesemeyer;Charles A. Weibel
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文献类型：
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作者：
Christian Haesemeyer;Charles A. Weibel
本章讨论上同调运算。虽然Motivic上同调最初是定义在完美域𝑘上的光滑簇上，但更有用的方法是将它看作定义在前面第12章所讨论的指向𝔸1-同伦范畴HO·上的函子。在定义了上同调运算并给出了几个例子之后，本章转向对Motivic Steenrod运算的公理处理。然后介绍了Motitive Milnor操作。此后，本章利用度映射𝑄𝑖证明了Milnor运算的序列Σ𝔛是依附于ROST变种𝑋的悬挂𝑡𝒩的约化上同调。它以沃沃茨基的动机度定理作为结论。
This chapter concerns cohomology operations. Although motivic cohomology was originally defined for smooth varieties over the perfect field 𝑘, it is more useful to view it as a functor defined on the pointed 𝔸1-homotopy category Ho ·, discussed previously in chapter 12. After defining cohomology operations and giving a few examples, the chapter turns to an axiomatic treatment of the motivic Steenrod operations. The motivic Milnor operations are then presented. Thereafter, this chapter demonstrates that the sequence of Milnor operations 𝑄𝑖 is exact on the reduced cohomology of the suspension Σ𝔛 attached to a Rost variety 𝑋, using the degree map 𝑡𝒩. It concludes with Voevodsky's motivic degree theorem.