Birational Motives, I
Birational Motives, I
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双理性动机，我
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R. Sujatha
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作者：
R. Sujatha
在这篇文章中，我们试图调和代数几何中的两个重要概念：动机和双有理几何。这样做的原因有很多;最初促使我们从动机的角度理解非分歧上同调的原因之一。虽然这一点在本文中还没有实现（但见本导言末尾的（2）），但它使我们得到了相当大的发展和令人惊讶的结构定理。关于我们理论的一个基本部分在有限域上的函数域上的应用，见[18]。为了使读者对我们的结果有一个简短的了解，我们假定读者熟悉Voevodsky关于动机的三角范畴的构造，并回忆起范畴的自然交换图
In this article, we try to conciliate two important ideas in algebraic geometry: motives and birational geometry. There are many reasons to do this; the one which motivated us originally was to understand unramified cohomology from a motivic point of view. Although this is not yet achieved in this paper (but see (2) at the end of this introduction), it led us to rather large developments and surprising structure theorems. For an application of an elementary part of our theory to function fields over finite fields, see [18]. In order to give the reader a brief resumé of our results, we assume familiarity with Voevodsky’s construction of his triangulated categories of motives and recall the naturally commutative diagram of categories