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lefschetz formula

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K-theoretic exceptional collections at roots of unity
A. Polishchuk
Journal:

Journal of K-Theory / Volume 7 / Issue 1 / February 2011

Published online by Cambridge University Press:

11 May 2010, pp. 169-201

Print publication:

February 2011
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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.