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A derived equivalence for a degree 6 del Pezzo surface over an arbitrary field

Published online by Cambridge University Press:  20 January 2011

M. Blunk ,
S.J. Sierra  and
S. Paul Smith
M. Blunk
Affiliation:
Department of Mathematics, The University of British Columbia Room 121, 1984 Mathematics Road Vancouver, B.C. V6T 1Z2, Canada, mblunk@math.ubc.ca
S.J. Sierra
Affiliation:
Princeton University, Department of Mathematics, Fine Hall, Washington Road Princeton, NJ 08544-1000, USA, ssierra@princeton.edu
S. Paul Smith
Affiliation:
Department of Mathematics, Box 354350, Univ. Washington Seattle, WA 98195, USA, smith@math.washington.edu
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Abstract

Let S be a degree six del Pezzo surface over an arbitrary field F. Motivated by the first author's classification of all such S up to isomorphism [3] in terms of a separable F-algebra B×Q×F, and by his K-theory isomorphism Kn(S) ≅ Kn(B×Q×F) for n ≥ 0, we prove an equivalence of derived categories

where A is an explicitly given finite dimensional F-algebra whose semisimple part is B×Q×F.

Keywords

Derived equivalencedel Pezzo surfacearbitrary field
Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 3 , December 2011 , pp. 481 - 492
Copyright
Copyright © ISOPP 2010

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