使用Tannakian形式主义的Coleman积分

The Tannakian Formalism and the Langlands Conjectures

Let H be a connected reductive group over an algebraically closed field of characteristic zero, and let G be an abstract group. In this note we show that every homomorphism from the Grothendieck semiring of H to that of G which maps irreducible representations to irreducibles, comes from a group homomorphism from G to H. We also connect this result with the Langlands conjectures.

秩为1的Drinfeld模的Coleman幂级数和Wiles互易性

Coleman's power series and Wiles' reciprocity for rank 1 Drinfeld modules

本文介绍了秩为1的Drinfeld模的Coleman幂级数的形式，并应用它来表示和证明Wiles显式互易律在这种情况下的模拟。

附属于Coleman族伴随表示的代数$p$-进$L$-函数的因式分解：非临界情形

Factorization of Algebraic $p$-adic $L$-functions Attached to Adjoint Representations of Coleman Families: Non-critical Case

该研究针对模形式Coleman族伴随表示的代数$p$-进$L$-函数，借助多类数论工具证明含Selmer复形行列式的分解公式，建立$p$-进Artin形式体系并推广了前人结果至$p$-非平凡情形。