论文标题
Langlands参数的模量
Moduli of Langlands Parameters
论文作者
论文摘要
Let $F$ be a nonarchimedean local field of residue characteristic $p$, let $\hat{G}$ be a split reductive group over $\mathbb{Z}[1/p]$ with an action of $W_F$, and let $^LG$ denote the semidirect product $\hat{G}\rtimes W_F$.我们构造了langlands参数的模量空间$ w_f \ to {^lg} $，并表明它是有限类型的本地，并且在$ \ mathbb {z} [1/p] $上均为flat，并且它是一个减少的本地完整交叉点。我们给出该空间几何纤维的连接组件和不可约组件的参数，以及$ \ operline以上的总空间的连接组件的参数化{\ Mathbb {z}}}} [1/P] [1/p] $（在$ \ opphyses）和$ \ operline $ \ operline {Z} $ {z {Z} $ {Z { $ \ ell \ neq p $。在每种情况下，我们精确地显示了每个连接的组件如何识别连接到较小的拆分还原组方案的“主”连接的组件。最后，我们通过$ \ hat {g} $研究了该空间的git商，并完整地描述了其纤维的同态形态，并在反转一套明确的有限素数之后，仅根据$^lg $进行了明确的有限的素数。
Let $F$ be a nonarchimedean local field of residue characteristic $p$, let $\hat{G}$ be a split reductive group over $\mathbb{Z}[1/p]$ with an action of $W_F$, and let $^LG$ denote the semidirect product $\hat{G}\rtimes W_F$. We construct a moduli space of Langlands parameters $W_F \to {^LG}$, and show that it is locally of finite type and flat over $\mathbb{Z}[1/p]$, and that it is a reduced local complete intersection. We give parameterizations of the connected components and the irreducible components of the geometric fibers of this space, and parameterizations of the connected components of the total space over $\overline{\mathbb{Z}}[1/p]$ (under mild hypotheses) and over $\overline{\mathbb{Z}}_{\ell}$ for $\ell\neq p$. In each case, we show precisely how each connected component identifies with the "principal" connected component attached to a smaller split reductive group scheme. Finally we study the GIT quotient of this space by $\hat{G}$ and give a complete description of its fibers up to homeomorphism, and a complete description of its ring of functions after inverting an explicit finite set of primes depending only on $^LG$.
