An introduction to derived (algebraic) geometry

Abstract

Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly in characteristic $0$, but we also see the tweaks which extend most of the content to analytic and differential settings.

arXiv comment100pp; v2 minor changes; v3 minor additions, mostly references; v4 minor additions and corrections; v5 comprehensively tidied with small additions, final version to appear in Rendiconti

References in corpus (15)

• Lie theory for nilpotent L-infinity algebras
• Higher and derived stacks: a global overview
• Derived Algebraic Geometry V: Structured Spaces
• Algebraic (geometric) $n$-stacks
• Completions and derived de Rham cohomology
• Semiregularity as a consequence of Goodwillie's theorem
• Differential Graded Schemes II: The 2-category of Differential Graded Schemes
• Grothendieck topologies from unique factorisation systems
• Loop Spaces and Langlands Parameters
• Notes characterising higher and derived stacks concretely
• Lectures on infinity categories
• Non-commutative derived moduli prestacks
• Augmented Homotopical Algebraic Geometry
• Non-abelian reciprocity laws and higher Brauer-Manin obstructions
• On Infinity Topoi