### Abstract

Original language | Undefined/Unknown |
---|---|

Journal | arXiv |

Publication status | Published - May 15 2018 |

### Keywords

- math.AC
- 13D02, 18G35

### Cite this

**Homotopy categories of unbounded complexes of projective modules.** / Yoshino, Yuji.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Homotopy categories of unbounded complexes of projective modules

AU - Yoshino, Yuji

N1 - Some notations are changed, Typos are corrected

PY - 2018/5/15

Y1 - 2018/5/15

N2 - We develop in this paper a stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As a result of the stable theory we are able to prove that a complex of finitely generated projective modules over a generically Gorenstein ring is exact if and only if its dual complex is exact. This shows the dependence of total reflexivity conditions for modules over a generically Gorenstein ring.

AB - We develop in this paper a stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As a result of the stable theory we are able to prove that a complex of finitely generated projective modules over a generically Gorenstein ring is exact if and only if its dual complex is exact. This shows the dependence of total reflexivity conditions for modules over a generically Gorenstein ring.

KW - math.AC

KW - 13D02, 18G35

M3 - Article

JO - arXiv

JF - arXiv

ER -