AI 中文总结
本文推广Deligne--Lusztig理论至paraductive群，计算其Tate上同调下界，并应用模函子性计算非奇异深度0尖点表示的L-参数。
AI 中文摘要
我们将Deligne--Lusztig理论推广到某些（可能无限型的）不连通约化群，这些群来自Bruhat--Tits建筑中点稳定子的特殊纤维，我们称之为“paraductive”群。然后，我们计算了paraductive群表示的Tate上同调的显式下界，并将其与Shintani下降、Lusztig限制和Glauberman对应联系起来。作为应用，利用Feng的模函子性和Scholze的ℓ独立性，我们计算了非阿基米德局部域上（可能狂分歧的）约化群的非奇异深度0尖点表示的Fargues--Scholze L-参数。
英文摘要
We develop an extension of Deligne--Lusztig theory to certain (possibly infinite type) disconnected reductive groups arising from the special fibers of point stabilizers in the Bruhat--Tits building, which we call \emph{paraductive}. We then compute explicit lower bounds for the Tate cohomology of representations of paraductive groups, relating these to Shintani descent, Lusztig restriction, and the Glauberman correspondence. As an application, using Feng's modular functoriality and Scholze's independence of $\ell$, we compute the Fargues--Scholze L-parameters of non-singular depth $0$ cuspidal representations of a (possibly wildly ramified) reductive group over a nonarchimedean local field.
Comments46 pages, comments welcome!
