论文标题
非常通用的混合杂货结构的Mumford-Tate组的一项根基，固定相关分级
The unipotent radical of the Mumford-Tate group of a very general mixed Hodge structure with a fixed associated graded
论文作者
论文摘要
给定理性矢量空间上的所有混合杂货结构的家族$ m_ \ mathbb {q} $带有固定重量过滤$ w_ \ cdot $和固定相关的分级霍奇结构$ gr^wm $自然是与复杂的亲属空间的一种对应。我们研究了家族非常普遍的芒福德州群体的根本性。我们通过使用一般的坦纳基式结果来做到这一点，该结果将过滤的坦纳基人类别中对象的基本组的单位激进与来自过滤的对象的扩展类别相关联。我们的主要结果表明，如果$ gr^wm $是两极分化并满足某些条件，那么在参数化仿射空间的许多适当的Zariski封闭式封闭式之外，该家族中的Mumford-Tate对象的一项单位激进的群体是$ GL（M _ MATHBB $ fin fin fin fin fin）的单位群体等于$ M_ \ MATHBB {Q} $（换句话说，超出了许多适当的Zariski封闭的结合，蒙福德 - 州群体的一能力群体与人们希望成为的一单位力量一样大）。请注意，这里$ gr^wm $本身可能有一个小的amumford-tate组。
The family of all mixed Hodge structures on a given rational vector space $M_\mathbb{Q}$ with a fixed weight filtration $W_\cdot$ and a fixed associated graded Hodge structure $Gr^WM$ is naturally in a one to one correspondence with a complex affine space. We study the unipotent radical of the very general Mumford-Tate group of the family. We do this by using general Tannakian results which relate the unipotent radical of the fundamental group of an object in a filtered Tannakian category to the extension classes of the object coming from the filtration. Our main result shows that if $Gr^WM$ is polarizable and satisfies some conditions, then outside a union of countably many proper Zariski closed subsets of the parametrizing affine space, the unipotent radical of the Mumford-Tate group of the objects in the family is equal to the unipotent radical of the parabolic subgroup of $GL(M_\mathbb{Q})$ associated to the weight filtration on $M_\mathbb{Q}$ (in other words, outside a union of countably many proper Zariski closed sets the unipotent radical of the Mumford-Tate group is as large as one may hope for it to be). Note that here $Gr^WM$ itself may have a small Mumford-Tate group.
