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• CommentRowNumber1.
• CommentAuthorTim_Porter
• CommentTimeApr 7th 2014
• (edited Apr 7th 2014)

Probably we need a separate forum discussion for linear topological ring as otherwise it may get confusing over at completion of a ring.

Zoran: thanks for the amendment. I was mostly interested in getting something down as a start, so did not explore the possiblities very much.

You mentioned pseudocompact rings and formal schemes. Can you start up an entry heading in that direction. I had an idea of writing something on Grothendieck categories and their duals (Oberst’s paper) in an attempt to look at the relationship between pseudocompact rings and duality, but you may know more on this than I do.

For formal schemes are you meaning in ordinary Alg. Geom or NCG?

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeApr 7th 2014
• (edited Apr 7th 2014)

I mean commutative algebraic geometry. SGA (I think in SGA3)…Grothendieck and Gabriel of course.

The discussion on pseudocompact rings does belong more to the questions of completion or rings than to the discussion of the subject of linear topologies aka uniform filters (the latter has main interest in noncommutative algebra and geometry)!

• CommentRowNumber3.
• CommentAuthorTim_Porter
• CommentTimeApr 7th 2014

My main interest in pseudocompact rings is that the completed group rings of pro-finite groups have this form. (I am vaguely wondering about Hopf-like structures on them.)

• CommentRowNumber4.
• CommentAuthorTim_Porter
• CommentTimeApr 11th 2014

• CommentRowNumber5.
• CommentAuthorzskoda
• CommentTimeApr 19th 2014

New entries Gabriel-Oberst duality and colocalization under construction. Content welcome, but please do not add various formatting balast before the construction is finished, as my internet connection is not good.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeApr 19th 2014

1. Added: “Note that if $R$ is commutative then (i) implies (UF).”