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.
Mayank Kumar Bijay (Thu,) studied this question.