Talk:Flat topology

Something wrong: quasi-finite is not part of the definition of fppf or fpqc[edit]

The person who wrote this seems to have confused fpqf with fppf or fpqc.--131.111.145.118 (talk) 16:40, 2 February 2011 (UTC)[reply]

Quasifinite is in the definition the fppf site in SGA 3, T1, Exp.4.6, pages 244-45. Colin McLarty (talk) 16:47, 9 July 2012 (UTC)[reply]

It seems that this was confused in SGA III, too. See for instance Prop. 6.3.1 (iv) in Exp IV, where this is mixed up. I corrected the definition. 192.52.15.64 (talk) 13:40, 30 April 2014 (UTC)[reply]

I changed the definition back, since there is a comment yet in the text, that the definition given leads to the same TOPOLOGY, which is true. It is however confusing because usually the notion "fppf-SITE" already refers to a different set of coverings (in which the 'quasi-finiteness' is not required). The main authors of the article should maybe change this. 192.52.15.64 (talk) 14:15, 30 April 2014 (UTC)[reply]

Definition of covers and topologies[edit]

In this article the (pre)topology is generated by coverings of affine schemes, where the covers are by definition finite. In every section it is then noted that this is not equivalent to the topology generated by such covers over arbitrary schemes. However, I do not see why this is easier than simply defining covers to be arbitrary families of fppf- or fpqc-morphisms and generating the topology by such covers over arbitrary schemes? Nmdwolf (talk) 22:30, 30 August 2022 (UTC)[reply]