论文标题
在本地功能字段上的刚性内部形式
Rigid inner forms over local function fields
论文作者
论文摘要
我们将[KAL16]在[KAL16]中定义的刚性内部形式的概念概括为本地功能字段$ f $的设置，顺序说明本地Langlands的猜想，用于$ f $的任意连接的还原组。为此，我们为连接的还原组$ g $定义了$ f $ a $ f $ a新的共同体套件$ h^{1}（\ nathcal {e}，z \ to g）\ g）\ subset h _ {\ text {fpqc}}}}}}^{1}^{1}（1} {1}（ $ h _ {\ text {fppf}}}^{2}（f，u）$中的一个类，用于某个规范定义的profinite换向组方案$ u $，构成了经典tate-nakayama duality theorem的类似物。 We define a relative transfer factor for an endoscopic datum serving a connected reductive group $G$ over $F$, and use rigid inner forms to extend this to an absolute transfer factor, enabling the statement of endoscopic conjectures relating stable virtual characters and $\dot{s}$-stable virtual characters for a semisimple $\dot{s}$ associated to a tempered Langlands parameter.
We generalize the concept of rigid inner forms, defined by Kaletha in [Kal16], to the setting of a local function field $F$ in order state the local Langlands conjectures for arbitrary connected reductive groups over $F$. To do this, we define for a connected reductive group $G$ over $F$ a new cohomology set $H^{1}(\mathcal{E}, Z \to G) \subset H_{\text{fpqc}}^{1}(\mathcal{E}, G)$ for a gerbe $\mathcal{E}$ attached to a class in $H_{\text{fppf}}^{2}(F, u)$ for a certain canonically-defined profinite commutative group scheme $u$, building up to an analogue of the classical Tate-Nakayama duality theorem. We define a relative transfer factor for an endoscopic datum serving a connected reductive group $G$ over $F$, and use rigid inner forms to extend this to an absolute transfer factor, enabling the statement of endoscopic conjectures relating stable virtual characters and $\dot{s}$-stable virtual characters for a semisimple $\dot{s}$ associated to a tempered Langlands parameter.
