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arXiv · 0809.1194

K-theoretic exceptional collections at roots of unity

Alexander Polishchuk
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Abstract

Using cyclotomic specializations of the equivariant $K$-theory with respect to a torus action we derive congruences for discrete invariants of exceptional objects in derived categories of coherent sheaves on a class of varieties that includes Grassmannians and smooth quadrics. For example, we prove that if $X={\Bbb P}^{n_1-1}\times...\times{\Bbb P}^{n_k-1}$, where $n_i$'s are powers of a fixed prime number $p$, then the rank of an exceptional object on $X$ is congruent to $\pm 1$ modulo $p$.

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Alexander Polishchuk. 2008-09-06. K-theoretic exceptional collections at roots of unity. https://arxiv.org/abs/0809.1194

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