Flat quasi-coherent sheaves of finite cotorsion dimension
2017 ◽
Vol 16
(01)
◽
pp. 1750015
Keyword(s):
Let [Formula: see text] be a quasi-compact and semi-separated scheme. If every flat quasi-coherent sheaf has finite cotorsion dimension, we prove that [Formula: see text] is [Formula: see text]-perfect for some [Formula: see text]. If [Formula: see text] is coherent and [Formula: see text]-perfect (not necessarily of finite Krull dimension), we prove that every flat quasi-coherent sheaf has finite pure injective dimension. Also, we show that there is an equivalence [Formula: see text] of homotopy categories, whenever [Formula: see text] is the homotopy category of pure injective flat quasi-coherent sheaves and [Formula: see text] is the pure derived category of flat quasi-coherent sheaves.
2007 ◽
Vol 186
◽
pp. 119-155
◽
Keyword(s):
2014 ◽
Vol 22
(2)
◽
pp. 51-56
2018 ◽
Vol 149
(1)
◽
pp. 15-43
◽
Keyword(s):
2019 ◽
Vol 19
(06)
◽
pp. 2050117
2020 ◽
Vol 296
(3-4)
◽
pp. 1387-1427
◽
2001 ◽
Vol 56
(3)
◽
pp. 592-594
◽