Dirac geometry II: coherent cohomology
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Dirac geometry II : coherent cohomology. / Hesselholt, Lars; Pstrągowski, Piotr.
I: Forum of Mathematics, Sigma, Bind 12, e27, 2024.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Dirac geometry II
T2 - coherent cohomology
AU - Hesselholt, Lars
AU - Pstrągowski, Piotr
N1 - Publisher Copyright: © The Author(s), 2024.
PY - 2024
Y1 - 2024
N2 - Dirac rings are commutative algebras in the symmetric monoidal category of Z-graded abelian groups with the Koszul sign in the symmetry isomorphism. In the prequel to this paper, we developed the commutative algebra of Dirac rings and defined the category of Dirac schemes. Here, we embed this category in the larger ∞-category of Dirac stacks, which also contains formal Dirac schemes, and develop the coherent cohomology of Dirac stacks. We apply the general theory to stable homotopy theory and use Quillen’s theorem on complex cobordism and Milnor’s theorem on the dual Steenrod algebra to identify the Dirac stacks corresponding to MU and Fp in terms of their functors of points. Finally, in an appendix, we develop a rudimentary theory of accessible presheaves.
AB - Dirac rings are commutative algebras in the symmetric monoidal category of Z-graded abelian groups with the Koszul sign in the symmetry isomorphism. In the prequel to this paper, we developed the commutative algebra of Dirac rings and defined the category of Dirac schemes. Here, we embed this category in the larger ∞-category of Dirac stacks, which also contains formal Dirac schemes, and develop the coherent cohomology of Dirac stacks. We apply the general theory to stable homotopy theory and use Quillen’s theorem on complex cobordism and Milnor’s theorem on the dual Steenrod algebra to identify the Dirac stacks corresponding to MU and Fp in terms of their functors of points. Finally, in an appendix, we develop a rudimentary theory of accessible presheaves.
U2 - 10.1017/fms.2024.2
DO - 10.1017/fms.2024.2
M3 - Journal article
AN - SCOPUS:85186888728
VL - 12
JO - Forum of Mathematics, Sigma
JF - Forum of Mathematics, Sigma
SN - 2050-5094
M1 - e27
ER -
ID: 390287980