Vol. 5, No. 3, 2011

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ISSN: 1944-7833 (e-only)
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Reflexivity and rigidity for complexes, II Schemes

Luchezar Avramov, Srikanth B. Iyengar and Joseph Lipman

Vol. 5 (2011), No. 3, 379–429
Abstract

We prove basic facts about reflexivity in derived categories over noetherian schemes, and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with respect to semidualizing complexes, in particular, relative dualizing complexes for Gorenstein-perfect maps. Our results include theorems of Yekutieli and Zhang concerning rigid dualizing complexes on schemes. This work is a continuation of part I (Algebra and Number Theory 4:1 (2010), 47–86), which dealt with commutative rings.

Keywords
perfect complexes, G-perfect complexes, Gorenstein-perfect, relative dualizing complexes, reflexivity, rigidity, semidualizing complexes
Mathematical Subject Classification 2000
Primary: 14A15, 14B25
Secondary: 13D05
Milestones
Received: 5 May 2010
Accepted: 24 August 2010
Published: 10 September 2011
Authors
Luchezar Avramov
Department of Mathematics
203 Avery Hall
University of Nebraska
Lincoln, NE 68588
United States
Srikanth B. Iyengar
Department of Mathematics
302.1 Avery Hall
University of Nebraska
Lincoln, NE 68588
United States
http://www.math.unl.edu/~siyengar2
Joseph Lipman
Purdue University
Department of Mathematics
150 North University Street
West Lafayette, IN 47907
United States
http://www.math.purdue.edu/~lipman/