论文标题
在具有有限域的严格多项式函子上
On strict polynomial functors with bounded domain
论文作者
论文摘要
我们介绍了一个新的函子类别：$ \ nathcal {p} _ {d，n} $ of Strict polyenmial functors temply多项式函数，并在特征$ p> 0 $的字段上由$ n $ dem $ d $限制。它等同于Schur代数$ s（n，d）$上有限维模块的类别，因此，它允许人们将函数类别中可用工具应用于代数组$ \ operatateNAme $ \ operatatorNamame {gl} _n $。我们详细研究了$ {\ cal p} _ {d，n} $的同源代数，以$ d = p $，并在稳定同型理论中的范围较低的spanthead duality中建立了$ {\ cal p} _ {\ cal p} _ {\ cal p} _ {\ cal p} _ {\ cal p} _的某些等价。
We introduce a new functor category: the category $\mathcal{P}_{d,n}$ of strict polynomial functors with bounded by $n$ domain of degree $d$ over a field of characteristic $p>0$. It is equivalent to the category of finite dimensional modules over the Schur algebra $S(n,d)$, hence it allows one to apply the tools available in functor categories to representations of the algebraic group $\operatorname{GL}_n$. We investigate in detail the homological algebra in ${\cal P}_{d,n}$ for $d=p$ and establish equivalences between certain subcategories of ${\cal P}_{d,n}$'s which resemble the Spanier-Whitehead duality in stable homotopy theory.
