标题： $\ell$-模局部theta对应 显示英文标题

标题： The $\ell$-modular local theta correspondence

摘要： 我们研究在模表示论的背景下，非阿基米德局部域上的局部θ对应的有效性，对于系数域为正特征的表示，\textit{即}。对于一个对称-正交或酉-酉对偶对，在$p$-adic域上，只要系数域的特征足够大，相对于对偶对的大小，我们得到一个双射对应，并称之为模局部θ对应。 显示英文摘要

摘要： We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a symplectic-orthogonal or a unitary-unitary dual pair over a $p$-adic field, we obtain a bijective correspondence, as long as the characteristic of the coefficient field is large enough compared to the size of the dual pair, and call it the modular local theta correspondence.