Author

Yu Shen

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Preprint Aug 2026

Cartan Determinants in algebraic geometry

We formulate a dg-categorical analogue of the Cartan determinant conjecture using numerical Grothendieck groups. Let $D$ be a smooth proper dg category over an algebraically closed field $k$. The Euler pairing on $K_0(D)$ descends to a nondegenerate bilinear form on the numerical Grothendieck group $K_{\mathrm{num}}(D)...

Ye-Qin Liu, Yu Shen, Zi-Yu Zhang · 0 citations

Preprint Aug 2026

A counterexample to a global-dimension bound for weighted projective lines

We observe that standard derived equivalences give a counterexample to a conjecture of Kalck on global dimension for weighted projective lines. For the root stack $X=\mathbb{P}^1\langle \infty,0,1;2,3,3\rangle$ we exhibit a $13$-dimensional radical-square-zero algebra $A$ such that $$ D^b(\mathrm{coh}X)\simeq D^b(\math...

Bochao Kong, Ye-Qin Liu, Yu Shen · 0 citations