论文标题
ARTIN异常的滑轮
Artin perverse sheaves
论文作者
论文摘要
我们表明，不正当的t结构在类别上诱导了t结构$ \ mathcal {d}^a（s，s，\ mathbb {z} _ \ ell）$的artin $ \ ell $ adic complectes的$当$ \ ell $ sadic complectes的$ s $是一个比$ 2 $的优秀尺寸的优秀方案，并提供$ 2 $的优秀方案。可以在$ 1 $维度方案的情况下明确描述此T结构的心脏$ \ mathrm {perv}^a（s，\ mathbb {z} _ \ ell）$。 当$ s $在有限字段上是有限类型时，我们还构建了$ \ mathcal {d}^a（s，s，\ mathbb {q} _ \ ell）$上的不正当同型t结构，并表明它是分配t结构的最佳近似值。我们描述其心脏的简单对象$ \ mathrm {perv}^a（s，\ mathbb {q} _ \ ell）^\＃$ $ $，并表明无重量的截断函数$ω^0 $是t-exact。我们还表明，失重的交点复合物$ ec_s =ω^0 ic_s $是一个简单的Artin同型合适的捆绑。如果$ s $是表面，它也是一个不正当的捆捆，但在不正当的滑轮类别中不必简单。
We show that the perverse t-structure induces a t-structure on the category $\mathcal{D}^A(S,\mathbb{Z}_\ell)$ of Artin $\ell$-adic complexes when $S$ is an excellent scheme of dimension less than $2$ and provide a counter-example in dimension $3$. The heart $\mathrm{Perv}^A(S,\mathbb{Z}_\ell)$ of this t-structure can be described explicitly in terms of representations in the case of $1$-dimensional schemes. When $S$ is of finite type over a finite field, we also construct a perverse homotopy t-structure over $\mathcal{D}^A(S,\mathbb{Q}_\ell)$ and show that it is the best possible approximation of the perverse t-structure. We describe the simple objects of its heart $\mathrm{Perv}^A(S,\mathbb{Q}_\ell)^\#$ and show that the weightless truncation functor $ω^0$ is t-exact. We also show that the weightless intersection complex $EC_S=ω^0 IC_S$ is a simple Artin homotopy perverse sheaf. If $S$ is a surface, it is also a perverse sheaf but it need not be simple in the category of perverse sheaves.
