Pan-Yue Zhou

A negative answer to a question on tilting objects and two-term complexes

Let $M$ be a silting object in an idempotent complete algebraic triangulated category $\mathcal T$. Put $B={\rm End}_{\mathcal T}(M)$, and let $\mathbb{P}_M\colon {\rm pr}(M)\to K^{[-1,0]}({\rm proj}B)$ be the presentation functor associated with $M$. It was recently asked whether $\mathbb{P}_M(T)$ must be tilting when...