论文标题
在全球字段上抬起和自动形式的Mod P Galois表示
Lifting and automorphy of reducible mod p Galois representations over global fields
论文作者
论文摘要
我们将上一篇论文的提升方法扩展到将可简化的奇数表示形式提升$ \barρ：\ mathrm {gal}（\ overline {f}/f）\ to g（k）$ g（k）$ of chevalley groups $ g（k）$ g（k）$。提升结果，与Wiles在数字场情况下率先率先启用的自动型提升结果以及在功能场情况下由Drinfeld和L. L. L. l. l. l. l. l. l. l. l. cood证明的全球Langlands对应的结果，提供了唯一的已知方法，可以访问Mod $ P $ PAGAIS代表模块化的可减少和不可降低案例的模块化。在可简化的情况下，这允许人们表明，实际表示，而不是仅仅是其半透明化，这是由于$ g $双重组上附加到cuspidal自动形态表示的几何表示形式的减少而产生的。作为一个特别具体的应用程序，我们获得了Serre的模块化猜想的版本，用于还原，奇数表示$ \barρ：\ Mathrm {gal}（\ Overline {\ Mathbb {Q}}}/\ Mathbb {Q}）在这种经典情况下，这扩展了Hamblen和Ramakrishna的早期结果，并证明了LOC未覆盖的固定字符的许多扩展的模块化。引用
We extend the lifting methods of our previous paper to lift reducible odd representations $\barρ:\mathrm{Gal}(\overline{F}/F) \to G(k)$ of Galois groups of global fields $F$ valued in Chevalley groups $G(k)$. Lifting results, when combined with automorphy lifting results pioneered by Wiles in the number field case and the results on the global Langlands correspondence proved by Drinfeld and L. Lafforgue in the function field case, give the only known method to access modularity of mod $p$ Galois representations in both reducible and irreducible cases. In the reducible case this allows one to show that the actual representation, rather than just its semisimplification, arises from reduction of the geometric representation attached to a cuspidal automorphic representation on the dual group of $G$. As a particularly concrete application, we get a version of Serre's modularity conjecture for reducible, odd representations $\barρ: \mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \to \mathrm{GL}_2(k)$. This extends earlier results of Hamblen and Ramakrishna in this classical case and proves modularity of infinitely many extensions of fixed characters that are not covered by loc. cit.
