Formal Derived Algebraic Geometry
Chang-Yeon Chough
TL;DR
This paper develops foundational aspects of formal derived algebraic geometry, connecting it with spectral algebraic geometry and proving a derived version of the formal GAGA theorem.
Contribution
It introduces foundational concepts for formal derived algebraic geometry and links it with spectral algebraic geometry, extending classical theorems to the derived setting.
Findings
Established a connection between derived and spectral algebraic objects.
Proved a version of the formal GAGA theorem in the derived context.
Developed foundational tools for formal derived algebraic geometry.
Abstract
We develop some foundations for the theory of formal derived algebraic geometry, which parallel the theory of formal spectral algebraic geometry by Jacob Lurie. For this, we establish a close connection between algebro-geometric objects in the derived and spectral settings. We apply this construction to prove a version of the formal GAGA theorem in the derived setting.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Polynomial and algebraic computation · Advanced Theoretical and Applied Studies in Material Sciences and Geometry