关于GL_3在一般情况下的模p局部-整体相容性
On mod p local-global compatibility for GL_3 in the ordinary case
摘要：
设F/F+是数域的CM扩张，其中素数p是完全分裂的，且每隔一个素数都是非分歧的。固定一个地方，|p的F。设rbar：Gal（F-bar/F）-> GL_3（Fp-bar）是一个连续的不可约伽罗瓦表示，使得|_{Gal（F_w-bar/F_w）}是上三角形的，最大不分裂的，通用的。如果rbar是自守的，并且一些适当的技术条件成立，我们证明了rbar|_{ \Gal（F_w-bar/F_w）}可以从紧酉群上模p自守形式空间上的GL_3（F_w）-作用恢复.在此过程中，我们证明了Serre猜想中关于rbar的权的结果，证明了rbar的普通提升的存在性，并证明了在这种情况下某些Taylor-Wiles修补模的自由性。我们还表明，存在许多伽罗瓦表示rbar，我们的主要定理适用。
英文摘要：
Suppose that F/F+ is a CM extension of number fields in which the prime p splits completely and every other prime is unramified. Fix a place w|p of F. Suppose that rbar : Gal(F-bar/F) -> GL_3(Fp-bar) is a continuous irreducible Galois representation such that rbar|_{Gal(F_w-bar/F_w)} is upper-triangular, maximally non-split, and generic. If rbar is automorphic, and some suitable technical conditions hold, we show that rbar|_{\Gal(F_w-bar/F_w)} can be recovered from the GL_3(F_w)-action on a space of mod p automorphic forms on a compact unitary group. On the way we prove results about weights in Serre's conjecture for rbar, show the existence of an ordinary lifting of rbar, and prove the freeness of certain Taylor-Wiles patched modules in this context. We also show the existence of many Galois representations rbar to which our main theorem applies.
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