论文标题
Kottwitz Gerbes的代表
Representations of the Kottwitz gerbes
论文作者
论文摘要
让$ f $为本地或全球领域，让$ g $为$ f $的线性代数组。我们研究了Kottwitz Gerbes $ \ text {rep}（\ text {kt} _ {f}）$的Tannakian类别和函数$ g \ mapsto b（f，g）$ [28]。特别是，我们表明，如果$ f $是$ \ mathbb {f} _q $的曲线的功能字段，则$ \ text {rep {rep}（\ text {kt} _f）$等于drinfeld isoshtukas的类别。对于数字字段，我们在$ \ text {rep}（\ text {kt} _ {\ Mathbb {q}}} $及其子类别上建立了各种纤维函子的存在及其子类别，并表明Scholze的猜想[41，猜测9.5]遵循完整的Tate Indecture tate tate tate Indeimente tate Indeimente tate Intefure tate tate Intefure firiture firite firite firite [47] [47] 47。
Let $F$ be a local or global field and let $G$ be a linear algebraic group over $F$. We study Tannakian categories of representations of the Kottwitz gerbes $\text{Rep}(\text{Kt}_{F})$ and the functor $G\mapsto B(F, G)$ defined by Kottwitz in [28]. In particular, we show that if $F$ is a function field of a curve over $\mathbb{F}_q$, then $\text{Rep}(\text{Kt}_F)$ is equivalent to the category of Drinfeld isoshtukas. In the case of number fields, we establish the existence of various fiber functors on $\text{Rep}(\text{Kt}_{\mathbb{Q}})$ and its subcategories and show that Scholze's conjecture [41, Conjecture 9.5] follows from the full Tate conjecture over finite fields [47].
