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- W3213317980 abstract "Let $mathcal{P}^{<infty} (Lambda$-mod$)$ be the category of finitely generated left modules of finite projective dimension over a basic Artin algebra $Lambda$. We develop an applicable criterion that reduces the test for contravariant finiteness of $mathcal{P}^{<infty} (Lambda$ -mod$)$ in $Lambda$-mod to corner algebras $e Lambda e$ for suitable idempotents $e in Lambda$. The reduction substantially facilitates access to the numerous homological benefits entailed by contravariant finiteness of $mathcal{P}^{<infty} (Lambda$-mod$)$. The consequences pursued hinge on the fact that this finiteness condition is known to be equivalent to the existence of a strong tilting object in $Lambda$-mod. We characterize the situation in which the process of strongly tilting $Lambda$-mod allows for arbitrary iteration: This occurs precisely when, in the strongly tilted module category mod-$widetilde{Lambda}$, the subcategory of modules of finite projective dimension is in turn contravariantly finite; the latter can, once again, be tested on suitable corners $e Lambda e$ of the original algebra $Lambda$. In the (frequently occurring) positive case, the sequence of consecutive strong tilts, $widetilde{Lambda}$, $ widetilde{widetilde{Lambda}}$, $widetilde{widetilde{widetilde{Lambda}}}, dots$, is shown to be periodic with period $2$ (up to Morita equivalence); moreover, any two adjacent categories in the sequence $mathcal{P}^{<infty} ( $mod-$widetilde{Lambda})$, $mathcal{P}^{<infty}(widetilde{widetilde{Lambda}}-mod)$, $mathcal{P}^{<infty}($ mod-$widetilde{widetilde{widetilde{Lambda}}}), dots$ are dual via contravariant Hom-functors induced by tilting bimodules which are strong on both sides." @default.
- W3213317980 created "2021-11-22" @default.
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- W3213317980 date "2021-11-17" @default.
- W3213317980 modified "2023-09-26" @default.
- W3213317980 title "Reduction techniques for contravariant finiteness and iterated strong tilting" @default.
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