论文标题
抛物线简单$ \ mathscr {l} $ - 不变
Parabolic Simple $\mathscr{L}$-Invariants
论文作者
论文摘要
令$ l $为$ \ mathbf {q} _p $的有限扩展名。令$ρ_l$为潜在的半稳定的非晶体$ p $ p $ - adic galois表示形式，以便相关的$ f $ semisimple weil-deligne表示绝对是不可塑性的。在本文中，我们研究了Fontaine-Mazur抛物线简单$ \ Mathscr {l} $ - $ρ_l$的不变式，该$以前仅在三角形案例中知道。基于Breuil抛物线简单$ \ Mathscr {l} $ - 不变的先前工作，我们附加到$ρ_l$ a本地$ \ Mathbf {q} _p $ -Analytic Teartional $π（ρ_l）$ of $ \ nathrm {gl） $ \ mathscr {l} $ - $ρ_l$的不变性。当$ρ_l$来自$ \ mathbf {g}（\ MathBb {a} _ {f^+}）$的修补自动形态表示（对于完全真实的$ f^+$ campact $ plos $ pp $ plmm plms $ plms plmm plmmat）我们在轻度假设中证明，$π（ρ_l）$是$ \ \ m athbf {g}（\ mathbf {g}（\ mathbb {\ mathb {a} _} _ {a} _ {f^+} $，这是等等的，$π（ρ_l）$是（$ p $ p $ - ad aid odymophic form）的hecke-异型子空间的子代表。 $ \ mathscr {l} $ - 不变性等于Fontaine-Mazur抛物线简单$ \ Mathscr {l} $ - 不变性。
Let $L$ be a finite extension of $\mathbf{Q}_p$. Let $ρ_L$ be a potentially semi-stable non-crystalline $p$-adic Galois representation such that the associated $F$-semisimple Weil-Deligne representation is absolutely indecomposable. In this paper, we study Fontaine-Mazur parabolic simple $\mathscr{L}$-invariants of $ρ_L$, which was previously only known in the trianguline case. Based on the previous work on Breuil's parabolic simple $\mathscr{L}$-invariants, we attach to $ρ_L$ a locally $\mathbf{Q}_p$-analytic representation $Π(ρ_L)$ of $\mathrm{GL}_{n}(L)$, which carries the information of parabolic simple $\mathscr{L}$-invariants of $ρ_L$. When $ρ_L$ comes from a patched automorphic representation of $\mathbf{G}(\mathbb{A}_{F^+})$ (for a define unitary group $\mathbf{G}$ over a totally real field $F^+$ which is compact at infinite places and $\mathrm{GL}_n$ at $p$-adic places), we prove under mild hypothesis that $Π(ρ_L)$ is a subrepresentation of the associated Hecke-isotypic subspace of the Banach spaces of (patched) $p$-adic automophic forms on $\mathbf{G}(\mathbb{A}_{F^+})$, this is equivalent to say that the Breuil's parabolic simple $\mathscr{L}$-invariants are equal to Fontaine-Mazur parabolic simple $\mathscr{L}$-invariants.
