Reflexivity and rigidity for complexes, II: Schemes

Avramov, Luchezar; Iyengar, Srikanth; Lipman, Joseph

doi:10.2140/ant.2011.5.379

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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

DOI: 10.2140/ant.2011.5.379

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/

Vol. 5, No. 3, 2011