A cotorsion theory in the homotopy category of flat quasi-coherent sheaves

Authors:
E. Hosseini and Sh. Salarian

Journal:
Proc. Amer. Math. Soc. **141** (2013), 753-762

MSC (2010):
Primary 18E30, 16E40, 16E05, 13D05, 14F05

DOI:
https://doi.org/10.1090/S0002-9939-2012-11364-4

Published electronically:
August 7, 2012

MathSciNet review:
3003669

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Abstract: Let be a Noetherian scheme, be the homotopy category of flat quasi-coherent -modules and be the homotopy category of all flat complexes. It is shown that the pair , - is a complete cotorsion theory in , where - is the essential image of the homotopy category of dg-cotorsion complexes of flat modules. Then we study the homotopy category ( - ). We show that in the affine case, this homotopy category is equal with the essential image of the embedding functor which has been studied by Neeman in his recent papers. Moreover, we present a condition for the inclusion ( - ) to be an equality, where is the essential image of the homotopy category of complexes of cotorsion flat sheaves.

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Additional Information

**E. Hosseini**

Affiliation:
Department of Mathematics, University of Isfahan, Isfahan, Iran

Email:
e.hosseini@sci.ui.ac.ir

**Sh. Salarian**

Affiliation:
Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran – and – School of Mathematics, Institute for Research in Fundamental Science (IPM), P.O. Box 19395-5746, Tehran, Iran

Email:
salarian@ipm.ir

DOI:
https://doi.org/10.1090/S0002-9939-2012-11364-4

Keywords:
Cotorsion theory,
quasi-coherent sheaves,
homotopy category,
adjoint functors,
dualizing complex

Received by editor(s):
May 8, 2011

Received by editor(s) in revised form:
July 11, 2011, and July 12, 2011

Published electronically:
August 7, 2012

Additional Notes:
This research was in part supported by a grant from IPM, No. 90130218

Communicated by:
Lev Borisov

Article copyright:
© Copyright 2012
American Mathematical Society