CrossRef Open Access 2024 2 sitasi

Finitistic dimensions over commutative DG-rings

Isaac Bird Liran Shaul Prashanth Sridhar Jordan Williamson

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Abstrak

AbstractIn this paper we study the finitistic dimensions of commutative noetherian non-positive DG-rings with finite amplitude. We prove that any DG-module M of finite flat dimension over such a DG-ring satisfies $${\textrm{proj}\,\textrm{dim}}_A(M) \le \dim (\textrm{H}^0 (A)) - \inf (M)$$ proj dim A ( M ) ≤ dim ( H 0 ( A ) ) - inf ( M ) . We further provide explicit constructions of DG-modules with prescribed projective dimension and deduce that the big finitistic projective dimension satisfies the bounds $$\dim (\textrm{H}^0 (A)) - {\text {amp}}(A) \le \textsf{FPD}(A) \le \dim (\textrm{H}^0(A))$$ dim ( H 0 ( A ) ) - amp ( A ) ≤ FPD ( A ) ≤ dim ( H 0 ( A ) ) . Moreover, we prove that DG-rings exist which achieve either bound. As a direct application, we prove new vanishing results for the derived Hochschild (co)homology of homologically smooth algebras.

Penulis (4)

Isaac Bird

Liran Shaul

Prashanth Sridhar

Jordan Williamson

Format Sitasi

APA MLA BibTeX

Bird, I., Shaul, L., Sridhar, P., Williamson, J. (2024). Finitistic dimensions over commutative DG-rings. https://doi.org/10.1007/s00209-024-03617-2

Akses Cepat

Lihat di Sumber doi.org/10.1007/s00209-024-03617-2

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Total Sitasi: 2×
Sumber Database: CrossRef
DOI: 10.1007/s00209-024-03617-2
Akses: Open Access ✓