论文标题
计数猜想和$ e $ $局部结构有限的还原组
Counting conjectures and $e$-local structures in finite reductive groups
论文作者
论文摘要
我们在广义的Harish-Chandra理论中证明了新的结果，该理论提供了所谓的Brauer- lusztig块的描述，从$ \ ell $ - adig-adig-deligne-lusztig品种中编码的信息方面。然后，我们通过考虑$ \ ell $ - 局部结构的几何类似物，提出了有限还原组的新猜想，这些类似物位于局部 - 全球计数猜想的核心。对于大型素数，由于Broué，Fong和Srinivasan在$ \ ell $ - 结构及其几何形状对应物之间建立的联系，我们的猜想与计数猜想相吻合。最后，使用上面提到的Brauer- lusztig块的描述，我们将猜想减少为Clifford理论特性的验证，从广义Harish-Chandra系列的某些参数化期望。
We prove new results in generalized Harish-Chandra theory providing a description of the so-called Brauer--Lusztig blocks in terms of the information encoded in the $\ell$-adic cohomology of Deligne--Lusztig varieties. Then, we propose new conjectures for finite reductive groups by considering geometric analogues of the $\ell$-local structures that lie at the heart of the local-global counting conjectures. For large primes, our conjectures coincide with the counting conjectures thanks to a connection established by Broué, Fong and Srinivasan between $\ell$-structures and their geometric counterpart. Finally, using the description of Brauer--Lusztig blocks mentioned above, we reduce our conjectures to the verification of Clifford theoretic properties expected from certain parametrisation of generalised Harish-Chandra series.
