论文标题
$ \ mathrm {gl} _ {2n} $的伊瓦沙瓦（Iwasawa）自动形式表示理论
Iwasawa theory of automorphic representations of $\mathrm{GL}_{2n}$ at non-ordinary primes
论文作者
论文摘要
让$π$为$ \ mathrm {gl} _ {2n}（\ Mathbb {a_q}）$的cuspidal自动形态表示，而让$ p $是$π$不受影响的奇数。在最近的一项工作中，Barrera，Dimitrov和Williams在非常见情况下构建了可能无限的$ P $ -ADIC $ L $ functions插值$ l $ l $ - 价值为$π$。在某些假设下，我们构建了两个\ textit {有限} $ p $ -adic $ l $ - $π$的功能，从而通过放松Pollack条件来扩展洛克伍德的早期作品。使用Langlands Local-Global兼容性，我们定义了$ p $ -Adic的循环组合$ \ Mathbb {q} $附加到$ p $ - adic-adic galois代表的代表的$ \ mathbb {q} $，并以kobayashi Pluls的精神为$ P $ p $ cy的iwasawa Main Insuperress cy-unipters cy-po $。
Let $Π$ be a cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb{A_Q})$ and let $p$ be an odd prime at which $Π$ is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded $p$-adic $L$-functions interpolating complex $L$-values of $Π$ in the non-ordinary case. Under certain assumptions, we construct two \textit{bounded} $p$-adic $L$-functions for $Π$, thus extending an earlier work of Rockwood by relaxing the Pollack condition. Using Langlands local-global compatibility, we define signed Selmer groups over the $p$-adic cyclotomic extension of $\mathbb{Q}$ attached to the $p$-adic Galois representation of $Π$ and formulate Iwasawa main conjectures in the spirit of Kobayashi's plus and minus main conjectures for $p$-supersingular elliptic curves.
