ℓ的独立性与上同调中的迹
Independence of ℓ and traces on cohomology.
作者信息
Olsson Martin
机构信息
Department of Mathematics, University of California, Berkeley, CA 94720
出版信息
Proc Natl Acad Sci U S A. 2016 May 10;113(19):5185-8. doi: 10.1073/pnas.1522140113. Epub 2016 Apr 13.
Abstract
Let k be an algebraically closed field, and let [Formula: see text] be an endomorphism of a separated scheme of finite type over k We show that for any [Formula: see text] invertible in k, the alternating sum of traces [Formula: see text] of pullback on étale cohomology is a rational number independent of [Formula: see text] This is deduced from a more general result for motivic sheaves.
摘要
设(k)为代数闭域，且设(\varphi)是(k)上有限型分离概型的一个自同态。我们证明，对于(k)中任何可逆的(t)， étale 上同调中拉回的迹(\text{Tr}(\varphi^*, H^i(X_{\bar{k}}, \mathbb{Q}_l)))的交错和是一个与(t)无关的有理数。这是从关于动机层的一个更一般的结果推导出来的。
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