The divided power algebra Div(k^∞) over a field of characteristic p is GL-coherent, and its bounded derived category of finitely presented modules has a semi-orthogonal decomposition into pieces generated by D^(r) ⊗ L_λ.
Generalizations of Stillman's conjecture via twisted commutative algebras
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Combining recent results on noetherianity of twisted commutative algebras by Draisma and the resolution of Stillman's conjecture by Ananyan-Hochster, we prove a broad generalization of Stillman's conjecture. Our theorem yields an array of boundedness results in commutative algebra that only depend on the degrees of the generators of an ideal, and not the number of variables in the ambient polynomial ring.
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GL-algebras in positive characteristic III: the divided power algebra
The divided power algebra Div(k^∞) over a field of characteristic p is GL-coherent, and its bounded derived category of finitely presented modules has a semi-orthogonal decomposition into pieces generated by D^(r) ⊗ L_λ.