论文标题
连贯的滑轮类别和倾斜模块的共同类别的共同结构
Co-$t$-structures on derived categories of coherent sheaves and the cohomology of tilting modules
论文作者
论文摘要
我们在一个还原组的nilpotent锥体$ \ Mathcal {n} $以及任何抛物线分辨率分辨率上的连贯滑轮类别上的nilpotent圆锥$ \ Mathcal {n} $上构建了一个共同结构。这些结构被用来表明沿（经典）弹簧分辨率的“异国奇特对象”的推动将在$ \ mathcal {n} $上的共同结构的coheart内部提供不可兼容的对象。我们还展示了各种抛物线共同结构如何通过向通常的翻译函数引入类似物来相关。作为一个应用程序，我们提供了方案理论的证明，该方案是对humphreys的相对汉弗莱斯的猜想，构成了$ p> h $的$ a $ a $ a $ a $ a $ a $ a $。
We construct a co-$t$-structure on the derived category of coherent sheaves on the nilpotent cone $\mathcal{N}$ of a reductive group, as well as on the derived category of coherent sheaves on any parabolic Springer resolution. These structures are employed to show that the push-forwards of the "exotic parity objects" along the (classical) Springer resolution give indecomposable objects inside the coheart of the co-$t$-structure on $\mathcal{N}$. We also demonstrate how the various parabolic co-$t$-structures can be related by introducing an analogue to the usual translation functors. As an application, we give a proof of a scheme-theoretic formulation of the relative Humphreys conjecture on support varieties of tilting modules in type $A$ for $p>h$.
