Talk:Formal scheme

Undefined notation in examples section

The `widetilde` notation used in the "Example" section doesn't seem to be defined anywhere in the article. So in the part discussing the I-adic topology on the ring A, it's not clear what the distinction is between the two structure sheaves ($\lim _{n}{\widetilde {A/I^{n}}}$ vs. $A/I$). The tilde is also used later to discuss ${\widetilde {\lim _{n}k[x,y]/I^{n}}}$.

If someone revisits this to define it, maybe they can expand the point being made in that paragraph as well?

Dzackgarza (talk) 03:28, 3 July 2021 (UTC)

Noetherian topological ring

Is it meant that the topological space is Noetherian, or that the underlying ring is Noetherian? Clearly the two are not equivalent, e.g. the topological ring $\mathbb{R}$ under the standard (Euclidean) topology. —Preceding unsigned comment added by 137.205.233.132 (talk) 11:14, 28 June 2010 (UTC)

Examples needed

This page should discuss the following two examples of formal schemes

• formal neighborhoods of an embedding $Y\hookrightarrow X$
• arithmetic deformations, especially with curves

The definition?

I think, that the definition of locally noetherian formal scheme given in this article is slightly misleading. In EGA I, Def. 10.4.2, they require, that every point has an open neighborhood, that is isomorphic to the formal spectrum of a noetherian adic ring. I think that this requirement is necessary to resolve the mentioned technical issues. The stalks of the formal spectrum of a noetherian adic ring are noetherian, for noetherian admissible rings I'm not sure. --Wandynsky (talk) 08:58, 2 June 2021 (UTC)

Formal geometry redirect?

I don't think formal geometry should've been directed here, because it's a common academic term to mean geometry studied (in primary/middle or grammar/high school) with proofs (as in Euclid's Elements) rather than geometry without them (informal geometry) and doesn't necessarily get to most/any the more advanced topics in this article (unless continued to college/university level)--dchmelik (t|c) 15:32, 13 July 2022 (UTC)