Deformation theory of representable morphisms of algebraic stacks

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Logarithmic Geometry and Moduli (2010, background): “Thus from ([50], 1.”
Coherent Tannaka duality and algebraicity of Hom-stacks (2014, result): “. 9.3]. A description of the automorphism, deformation and obstruction functors of Rep Z× SX/S in terms of the cotangent complex are given on [Hal14b, p. 37], which mostly follows from the results of [Ols06a]. That these functors are coherent is [Hal14a, Thm. C]. This completes the proof of (i). We ”
QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, background): “Stacks of representable morphisms to quotient stacks by reductive groups have canonical relative obstruction theories, by the same construction in [6] and a deformation result of Olsson [38].”
Logarithmic Gromov-Witten invariants (2011, background): “that all but the front and back faces of the cube are cartesian. Because M(X) → M is strict and representable standard obstruction theory applies to the extension problem of gto T¯ ([Il], Ch.III, and [Ol4] for the case of representable morphisms of stacks). Thus the obstructions class ω(g) ∈ Ext1 OT”
On the local quotient structure of Artin stacks (2009, background): “Deformation theory of G-torsors. We will need to know the deformation theory of G-torsors over Artin stacks. We recall for the reader the necessary results of the deformation theory of G-torsors from [Ols06a] and [AOV08]. Suppose G→ Sis a fppf group scheme and p: P → X is a G-torsor. Let i: X → X′ b”