The Moduli of Sections Has a Canonical Obstruction Theory

TL;DR

This paper proves that moduli stacks of sections over locally Noetherian bases have canonical obstruction theories, constructing necessary dualizing sheaves and trace maps for families of tame twisted curves.

Contribution

It provides a detailed proof of the existence of canonical obstruction theories for moduli stacks of sections, including the construction of dualizing sheaves and trace maps.

Findings

Moduli stacks of sections have canonical obstruction theories.

Constructed dualizing sheaves and trace maps for tame twisted curves.

Established foundational tools for deformation theory in this context.

Abstract

We give a detailed proof that locally Noetherian moduli stacks of sections carry canonical obstruction theories. As part of the argument we construct a dualizing sheaf and trace map, in the lisse-etale topology, for families of tame twisted curves, when the base stack is locally Noetherian.