论文标题
lafforgue伪chard和Galois代表限制的均等
Lafforgue pseudocharacters and parities of limits of Galois representations
论文作者
论文摘要
令$ f $为CM字段，具有完全真实的子字段$ f^+$，并且让$ c $ -c $ - algebraic cuspidal cuspidal自动形态自动形式表示$ \ mathrm {u}（a，a，b）（\ mathbf {a，a} _} _} _ {f^+}）的limimecterial commenterate（\ mathbf {a，mathbf {a，a}）。我们附加到$π$ a galois表示$r_π：\ mathrm {gal}（\ edlinef/ f/ f^+）\ to {}^c \ mathrm {u}（a，b）（\ overline {\ mathbf q} _ \ ell）ys $ conjugation $ conjugation $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ c $ r嗡嗡声 - 猜想。作为推论，我们推断出GALOIS表示与某些不规则的$ C $ -COUM-ALGEBRAIC（本质上是）共轭自二）自dual cuspidal cuspidal sutomorphic表示，$ \ mathrm {gl} _n（\ mathbf a_f）$在bellaïche-cheenevier中是奇怪的。
Let $F$ be a CM field with totally real subfield $F^+$ and let $π$ be a $C$-algebraic cuspidal automorphic automorphic representation of $\mathrm{U}(a,b)(\mathbf{A}_{F^+})$ whose archimedean components lie in the (non-degenerate limit of) discrete series. We attach to $π$ a Galois representation $R_π:\mathrm{Gal}(\overline F/ F^+)\to{}^C\mathrm{U}(a,b)(\overline{\mathbf Q}_\ell)$ such that, for any complex conjugation element $c$, $R_π(c)$ is as predicted by the Buzzard--Gee conjecture. As a corollary, we deduce that the Galois representations attached to certain irregular, $C$-algebraic (essentially) conjugate self-dual cuspidal automorphic representations of $\mathrm{GL}_n(\mathbf A_F)$ are odd in the sense of Bellaïche--Chenevier.
