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K-theoretic exceptional collections at roots of unity

Published online by Cambridge University Press:  11 May 2010

A. Polishchuk
A. Polishchuk
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97405, apolish@math.uoregon.edu
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Abstract

Using cyclotomic specializations of 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 , where the ni's are powers of a fixed prime number p, then the rank of an exceptional object on X is congruent to ±1 modulo p.

Keywords

Exceptional collectionequivariant K-theoryLefschetz formula
Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 1 , February 2011 , pp. 169 - 201
Copyright
Copyright © ISOPP 2010

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