Derived Algebraic Geometry

Lurie's derived schemes, spectral algebraic geometry, and shifted symplectic structures.


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Derived Algebraic Geometry. Lurie’s derived schemes, spectral algebraic geometry, and shifted symplectic structures.

Foundations and canonical references

The standard treatments of derived algebraic geometry approach the subject from complementary angles. Lurie, Higher Algebra (2017) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Toen, Derived Algebraic Geometry (2014) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for derived algebraic geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2017
    Higher Algebra
    lurie-2017
  • textbook · primary · 2014
    Derived Algebraic Geometry
    toen-2014

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