Period Map and Derived Invariants in Algebraic Geometry
Research Paper#Algebraic Geometry, Derived Categories, Deformation Theory🔬 Research|Analyzed: Jan 3, 2026 17:14•
Published: Dec 30, 2025 16:58
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•ArXivAnalysis
This paper investigates the relationship between deformations of a scheme and its associated derived category of quasi-coherent sheaves. It identifies the tangent map with the dual HKR map and explores derived invariance properties of liftability and the deformation functor. The results contribute to understanding the interplay between commutative and noncommutative geometry and have implications for derived algebraic geometry.
Key Takeaways
- •Establishes a connection between deformations of a scheme and its derived category.
- •Identifies the tangent map with the dual HKR map.
- •Proves derived invariance of liftability under certain conditions.
- •Exhibits cases where the deformation functor is a derived invariant.
Reference / Citation
View Original"The paper identifies the tangent map with the dual HKR map and proves liftability along square-zero extensions to be a derived invariant."