The Moduli of Sections Has a Canonical Obstruction Theory

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-étale topology, for families of tame twisted curves, when the base stack is locally Noetherian. Contents 10 4. Obstruction theories via the Fundamental Theorem 17 Appendix A. Three descent theorems for lisse-étale sheaves on algebraic stacks 24 Appendix B. Functoriality of the Fundamental Theorem 30 References 40