论文标题
$ \ ell $ - adic本地系统和GALOIS表示的派生分析模量上移动的符号结构
Shifted symplectic structures on derived analytic moduli of $\ell$-adic local systems and Galois representations
论文作者
论文摘要
我们基于匕首代数的DG增强对非架构的分析几何形状的表征。这使我们能够为多种类型的Pro-étale滑轮制定派生的分析模量函子，并使用算术偶性定理通过侵犯来构造它们在它们上的移位符号结构。为了处理涉及泰特曲折的偶性函数，我们在形式加权模量堆栈上引入了加权移动的符号结构，并通过服用$ \ m athbb {g} _m $ $ -invariants给出了通常的模量堆栈。 特别是，这确立了在$ \ ell $ - $ - $ - 亚种的构造构造复合物中的衍生模量堆栈上的转变的符号和拉格朗日结构的存在，并通过Poincaré二元性以及$ \ ell $ all $ - eeld $ aidic galois的衍生模量堆栈在光滑品种上的构造构造中的存在。后者证明了Minhyong Kim的猜想。 还以$ \ ell $ $ - ad-adic galois表示环环体字段$ k（μ_ {\ ell^{\ infty}}）$建立了未加权的符号和拉格朗日结构，但要符合与伊瓦沙瓦理论相关的其他约束；这些派生的模量堆栈产生了Selmer络合物的非亚洲类似物，并具有$ 0 $降低的与广义木薯（TACE-TATE配对）相关的符合符号结构。
We develop a characterisation of non-Archimedean derived analytic geometry based on dg enhancements of dagger algebras. This allows us to formulate derived analytic moduli functors for many types of pro-étale sheaves, and to construct shifted symplectic structures on them by transgression using arithmetic duality theorems. In order to handle duality functors involving Tate twists, we introduce weighted shifted symplectic structures on formal weighted moduli stacks, with the usual moduli stacks given by taking $\mathbb{G}_m$-invariants. In particular, this establishes the existence of shifted symplectic and Lagrangian structures on derived moduli stacks of $\ell$-adic constructible complexes on smooth varieties via Poincaré duality, and on derived moduli stacks of $\ell$-adic Galois representations via Tate and Poitou--Tate duality; the latter proves a conjecture of Minhyong Kim. Unweighted shifted symplectic and Lagrangian structures are also established for $\ell$-adic Galois representations of cyclotomic fields $K(μ_{\ell^{\infty}})$, subject to additional constraints related to Iwasawa theory; these derived moduli stacks yield a non-abelian analogue of Selmer complexes, with $0$-shifted symplectic structures related to generalised Cassels--Tate pairings.
