论文标题
派生抛物线诱导的左伴侣
The Left Adjoint of Derived Parabolic Induction
论文作者
论文摘要
我们证明，在$ p $ addic还原组的平滑mod $ p $表示的无界派生类别上定义的派生抛物线感应函数承认左伴随$ \ mathrm {l}（u， - ）$。我们在一些详细范围内研究了同时函数$ \ mathrm {h}^i \ circ \ mathrm {l}（u， - ）$，并推断出$ \ mathrm {l}（u， - ）$保留有界的复合物和施耐德 - 索森森（Schneider-Sorensen）的全球可理解性。使用$ \ mathrm {l}（u， - ）$，我们定义了一个派生的satake同构，证明它编码了赫兹格（Herzig）明确定义的mod $ p $ satake同构。
We prove that the derived parabolic induction functor, defined on the unbounded derived category of smooth mod $p$ representations of a $p$-adic reductive group, admits a left adjoint $\mathrm{L}(U,-)$. We study the cohomology functors $\mathrm{H}^i\circ \mathrm{L}(U,-)$ in some detail and deduce that $\mathrm{L}(U,-)$ preserves bounded complexes and global admissibility in the sense of Schneider--Sorensen. Using $\mathrm{L}(U,-)$ we define a derived Satake homomorphism und prove that it encodes the mod $p$ Satake homomorphisms defined explicitly by Herzig.
