Bondal's coherence conjecture for regular algebras

Let AA be a regular graded algebra, meaning that it has finite global dimension and satisfies the Gorenstein condition

ExtAi(kA,kA){0,id,k[l] for some lZ,i=d.\operatorname{Ext}^i_A(k_A,k_A)\cong\begin{cases}0,&i\ne d,\\ k[l]\text{ for some }l\in{\mathbb Z},&i=d. \end{cases}

The algebra AA is graded coherent if every finitely generated graded ideal is finitely presented. Bondal's coherence conjecture. Every regular algebra is graded coherent. The source says this conjecture is due to A. Bondal and gives no resolution.

Sources & referencesView supporting material

Primary source

Dmitri Piontkovski, “Coherent algebras and noncommutative projective lines”, arXiv:math/0606279 (2007).

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