What question did this study set out to answer?

The central aim is to formulate a generalized notion of Picard symplectic structures that accommodates Tate and motivic twists.

June 13, 2026Open Access

Picard Symplectic Structures and Moduli of ℓ-adic Local Systems

Key Points

The central aim is to formulate a generalized notion of Picard symplectic structures that accommodates Tate and motivic twists.
Developed concepts based on the theory of shifted symplectic structures
Applied these concepts to ℓ-adic moduli problems
Extended traditional structures to include Tate twists
Introduced a Picard symplectic structure that incorporates Tate and motivic twists into moduli problems.
Established connections between derived stacks and ℓ-adic structures via generalized closed 2-forms.

Abstract

The theory of shifted symplectic structures developed by Pantev–Toen–Vaquie–Vezzosi assigns to a derived stack Y in characteristic 0, a closed 2-form whose underlying pairing of tangent complex induces a shifted equivalence. The purpose of this note is to formulate a generalized notion which allows Tate twists and possibly, motivic twists to appear naturally, extending such structures to ℓ-adic moduli problems. We call the resulting structure a Picard symplectic structure.

Picard Symplectic Structures and Moduli of ℓ-adic Local Systems

Key Points

Abstract

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