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- W4381486836 abstract "Abstract The purpose of this paper and its sequel is to develop the geometry built from the commutative algebras that naturally appear as the homology of differential graded algebras and, more generally, as the homotopy of algebras in spectra. The commutative algebras in question are those in the symmetric monoidal category of graded abelian groups, and, being commutative, they form the affine building blocks of a geometry, as commutative rings form the affine building blocks of algebraic geometry. We name this geometry Dirac geometry, because the grading exhibits the hallmarks of spin in that it is a remnant of the internal structure encoded by anima , it distinguishes symmetric and anti-symmetric behavior, and the coherent cohomology of Dirac schemes and Dirac stacks, which we develop in the sequel, admits half-integer Serre twists. Thus, informally, Dirac geometry constitutes a “square root” of $$mathbb {G}_m$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> -equivariant algebraic geometry." @default.
- W4381486836 created "2023-06-22" @default.
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- W4381486836 date "2023-06-21" @default.
- W4381486836 modified "2023-10-14" @default.
- W4381486836 title "Dirac Geometry I: Commutative Algebra" @default.
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- W4381486836 doi "https://doi.org/10.1007/s42543-023-00072-6" @default.
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