K-theoretic exceptional collections at roots of unity

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dc.creatorPolishchuk, Alexander
dc.date2008-09-06
dc.date.accessioned2026-07-07T10:01:18Z
dc.date.available2026-07-07T10:01:18Z
dc.descriptionUsing 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 $p$.
dc.description20 pages. Preliminary version, comments are welcome
dc.identifierhttps://arxiv.org/abs/0809.1194
dc.identifierhttp://arxiv.org/abs/0809.1194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168590
dc.subjectAlgebraic Geometry
dc.subjectK-Theory and Homology
dc.titleK-theoretic exceptional collections at roots of unity
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