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- W3202165260 abstract "A commutative Noetherian ring R is said to be Tor-persistent if, for any finitely generated R-module M, the vanishing of ToriR(M,M) for i≫0 implies M has finite projective dimension. An open question of Avramov, et al. asks whether any such R is Tor-persistent. In this work, we exploit properties of exterior powers of modules and complexes to provide several partial answers to this question; in particular, we show that every local ring (R,m) with m3=0 is Tor-persistent. As a consequence of our methods, we provide a new proof of the Tachikawa Conjecture for positively graded rings over a field of characteristic different from 2." @default.
- W3202165260 created "2021-10-11" @default.
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- W3202165260 date "2022-04-01" @default.
- W3202165260 modified "2023-10-16" @default.
- W3202165260 title "Exterior powers and Tor-persistence" @default.
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- W3202165260 doi "https://doi.org/10.1016/j.jpaa.2021.106890" @default.
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