论文标题
在$ \ mathfrak {p}^{\ infty} $ - Quaternionic Hilbert Modular品种的$ \ mathfrak {p}^{\ inftrak {p}^{
On certain cohomology groups attached to $\mathfrak{p}^{\infty}$-towers of quaternionic Hilbert modular varieties
论文作者
论文摘要
对于一个完全真实的数字字段$ f $和一个非架构prime $ \ mathfrak {p} $ $ f $，位于素数上方$ p $上方，我们介绍了某些交织的共同学组，这些组合$ \ mathfrak {p}^{p}^{\ inftty} $ \ mathfrak {p} $和$ p $ - $ \ mbox {pgl} _2（f _ {\ mathfrak {p}}}）$的$ P $ - 适用于无限$ p $ p $ - ad的变形，以$ \ mathfrak {p} $的cuspidal自动形式表示的$π$的$ d^**（\ mathbb {a}）$，这产生了galois代表$ $ $ $ fo $ $ for的无限构造的自然构造。
For a totally real number field $F$ and a nonarchimedean prime $\mathfrak{p}$ of $F$ lying above a prime number $p$ we introduce certain sheaf cohomology groups that intertwine the $\mathfrak{p}^{\infty}$-tower of a quaternionic Hilbert modular variety associated to a quaternion algebra $D$ over $F$ that is split at $\mathfrak{p}$ and a $p$-adically admissible representation of $\mbox{PGL}_2(F_{\mathfrak{p}})$. Applied to infinitesimal $p$-adic deformations of the local factor at $\mathfrak{p}$ of a cuspidal automorphic representation $π$ of $D^*(\mathbb{A})$ this yields a natural construction of infinitesimal deformations of the Galois representation attached to $π$.
