论文标题
在Hecke代数的代数K理论上
On the algebraic K-theory of Hecke algebras
论文作者
论文摘要
考虑一个完全断开的G组，该组是循环循环的，即包含正常的紧凑型敞开亚组L，使得g/l是无限的循环。我们建立了一个王序列，该序列计算了G的Hecke代数的代数K组，并表明所有负K组都消失了。这证实了在此特殊情况下，G理论的Farrell-Jones猜想是G的Hecke代数。我们的最终长期目标是证明任何还原性P-ADIC组的任何封闭子组。本文的结果将在最终证明中发挥作用。
Consider a totally disconnected group G, which is covirtually cyclic, i.e., contains a normal compact open subgroup L such that G/L is infinite cyclic. We establish a Wang sequence, which computes the algebraic K-groups of the Hecke algebra of G in terms of the one of L, and show that all negative K-groups vanish. This confirms the K-theoretic Farrell-Jones Conjecture for the Hecke algebra of G in this special case. Our ultimate long term goal is to prove it for any closed subgroup of any reductive p-adic group. The results of this paper will play a role in the final proof.
