论文标题
有泰特纤维的家庭的动机分解：光滑而奇异的案例
Motivic decompositions of families with Tate fibers: smooth and singular cases
论文作者
论文摘要
我们将Wildeshaus的动机中间扩展理论应用于由Deninger-Murre和Corti-Hanamura提出的动机分解猜想。我们首先获得了一个普通的动机分解，用于任意光滑的投射家庭$ f：x \ rightarrow s $的动机，其几何纤维是泰特的。该公式使用Voevodsky的动机，对于任意的常规基本$ S $有效，而无需假设存在基本场，甚至存在Prime Integer $ \ ell $ conterible在$ s $上。这个结果以及邦托的一些思想，使我们对Corti-Hanamura的猜想进行了广泛的表述。其次，当$ f：x \ rightarrow s $是特征性$ 0 $ base上的一个投影二次束时，我们确定了动机分解的存在，该$ 0 $ base是足够通用的，或者其判别基因座是正常的交叉分隔线。这为在这种情况下的伯恩斯坦 - 比林森 - deligne分解提供了动机。
We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger-Murre and Corti-Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary smooth projective family $f:X \rightarrow S$ whose geometric fibers are Tate. Using Voevodsky's motives with rational coefficients, the formula is valid for an arbitrary regular base $S$, without assuming the existence of a base field or even of a prime integer $\ell$ invertible on $S$. This result, and some of Bondarko' ideas, lead us to a generalized formulation of Corti-Hanamura's conjecture. Secondly we establish the existence of the motivic decomposition when $f:X \rightarrow S$ is a projective quadric bundle over a characteristic $0$ base, which is either sufficiently general or whose discriminant locus is a normal crossing divisor. This provides a motivic lift of the Bernstein-Beilinson-Deligne decomposition in this setting.
