论文标题
汽车胶合
Automorphic Gluing
论文作者
论文摘要
我们证明了在几何兰兰兹通讯的自同形方面的粘合定理：大概说，我们表明$ \ m artrm {dmod}（\ sathrm {bunrm {bunrm {bunrm {bunrm {bun} _g）$及其完整的子类别$ \ mathrm {dmod}（dmod}（dmod）回火对象由类别$ \ mathrm {dmod}（\ Mathrm {bun} _m）^\ Mathrm {temp} $用于所有标准Levi子组$ M \ subsetneq g $。该定理旨在与光谱胶定理完全匹配，光谱胶定理发生在几何兰兰兹猜想的另一侧。在此过程中，我们指出并证明了一些可能具有独立利益的事实。例如，对于任何抛物线$ p \ subseteq g $，我们表明函数$ \ mathrm {ct} _ {p，*}：\ mathrm {dmod}（\ mathrm {bunrm {bun} _g） $ \ MATHRM {eis} _ {p，*}：\ Mathrm {dmod}（\ Mathrm {bun} _m）\ to \ Mathrm {dmod}（\ Mathrm {\ Mathrm {bun} _g） $ \ mathrm {eis} _ {p，！} $保留反粘的对象。
We prove a gluing theorem on the automorphic side of the geometric Langlands correspondence: roughly speaking, we show that the difference between $\mathrm{DMod}(\mathrm{Bun}_G)$ and its full subcategory $\mathrm{DMod}(\mathrm{Bun}_G)^\mathrm{temp}$ of tempered objects is compensated by the categories $\mathrm{DMod}(\mathrm{Bun}_M)^\mathrm{temp}$ for all standard Levi subgroups $M \subsetneq G$. This theorem is designed to match exactly with the spectral gluing theorem, an analogous result occurring on the other side of the geometric Langlands conjecture. Along the way, we state and prove several facts that might be of independent interest. For instance, for any parabolic $P \subseteq G$, we show that the functors $\mathrm{CT}_{P,*}:\mathrm{DMod}(\mathrm{Bun}_G) \to \mathrm{DMod}(\mathrm{Bun}_M)$ and $\mathrm{Eis}_{P,*}: \mathrm{DMod}(\mathrm{Bun}_M) \to \mathrm{DMod}(\mathrm{Bun}_G)$ preserve tempered objects, whereas the standard Eisenstein functor $\mathrm{Eis}_{P,!}$ preserves anti-tempered objects.
