On the Invertibility of Motives of Affine Quadrics
On the Invertibility of Motives of Affine Quadrics
复制标题
仿射二次曲面动机的可逆性
作者：
Tom Bachmann
证明了光滑仿射二次曲面的约化动机作为动机三角范畴Dm(k，zz[1/e])的对象是可逆的(其中k是具有指数特征e的完备域)。我们还建立了Po Hu关于某些仿射Pfister二次曲面乘积的猜想的一个动机版本。这两个结果都是通过研究DM(k，ZZ[1/e])上的一个新的守恒函子得到的，它的构造构成了本文工作的主要部分。
We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives DM(k, ZZ[1/e]) (where k is a perfect field of exponential characteristic e). We also establish a motivic version of the conjectures of Po Hu on products of certain affine Pfister quadrics. Both of these results are obtained by studying a novel conservative functor on (a subcategory of) DM(k, ZZ[1/e]), the construction of which constitutes the main part of this work.