[数学] 的Grothendieck环中某些环面类的计算 品种 [推广有奖]

摘要翻译：
根据变种Grothendieck环的λ结构，建立了Grothendieck环中某些环面类的公式。更明确地说，如果L*是n维可分K-代数L中可逆元的环面，则L*类可以表示为L的谱在λ运算下的像的交替和乘以Lefschetz类的幂。该公式是从环面的上同调出发提出的，说明了一种启发式方法，可用于其他情况。为了证明该公式，需要在Grothendieck环中进行一些相当显式的计算。为了得到这些，我们从k的绝对Galois群的Burnside环到k上变种的Grothendieck环引入了一个同态。在此过程中，我们得到了由零维变体产生的子带结构的一些信息。
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英文标题：
《The computation of the classes of some tori in the Grothendieck ring of
  varieties》
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作者：
Karl R\"okaeus
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最新提交年份：
2007
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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 establish a formula for the classes of certain tori in the Grothendieck ring of varieties, in terms of its lambda-structure. More explicitly, we will see that if L* is the torus of invertible elements in the n-dimensional separable k-algebra L, then the class of L* can be expressed as an alternating sum of the images of the spectrum of L under the lambda-operations, multiplied by powers of the Lefschetz class. This formula is suggested from the cohomology of the torus, illustrating a heuristic method that can be used in other situations. To prove the formula will require some rather explicit calculations in the Grothendieck ring. To be able to make these we introduce a homomorphism from the Burnside ring of the absolute Galois group of k, to the Grothendieck ring of varieties over k. In the process we obtain some information about the structure of the subring generated by zero-dimensional varieties.
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PDF链接：
https://arxiv.org/pdf/0708.4396