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Report on the finiteness of silting objects (2002.08534v2)
Published 20 Feb 2020 in math.RT and math.RA
Abstract: We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, one studies two classes of $\tau$-tilting-finite algebras and give the numbers of their two-term silting objects. Finally, we explore when $\tau$-tilting-finiteness implies representatoin-finiteness, and obtain several classes of algebras in which a $\tau$-tilting-finite algebra is representation-finite.
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