Talk:Cohomological dimension

Dimension 0 and semi-simple
The article states that the cohomological dimension of G with coeffs in a ring R is 0 if and only if R[G] is semi simple. But $$\mathbb{Z}$$[trivial group] is isomorphic to $$\mathbb{Z}$$, which is not semi-simple as a module over itself. Seamus Stoke (talk) 19:05, 22 January 2009 (UTC)
 * I confirm this is a mistake in the article, but I seem to remember something extremely similar is actually true. In particular, the part about the group order being a unit is right for cd 0, I am pretty sure.  So for instance Z[x,y]/(1-2x,y^2-1) is not semi-simple but is a group ring of  a cyclic group of order 2 where the group has cd 0.  Maybe the word semi-simple is just out of place.  I used Cartan–Eilenberg as a reference (which only covers finite groups) and some articles of Swan, so I haven't looked through the references in this article any time recently.  Here is the  where it was made.  It is probably true over fields.  I think the blocks should be semi-simple, but I'm not sure how to phrase that for general rings.  I think Jacobson semi-simple also does not work, since something like the 2-adics (as a group ring ovr the 2-adics of the trivial group) are not Jacobson semi-simple, but the trivial group does have cd 0.  JackSchmidt (talk) 19:42, 22 January 2009 (UTC)

Dimension and strict dimension
The definition for a group isn't quite right, since the modules are unrestricted, and so this is defining strict cd. They should be discrete torsion modules. This is from Serre I.3. I will expand this myself when I get a moment. Spectral sequence (talk) 06:23, 16 May 2013 (UTC)

Absolute Galois group of Laurent series
I don't think that the claim &quot; the field of laurent series $$ k((t)) $$ over an algebraically closed field k of non-zero characteristic also has absolute Galois group isomorphic to $$ \hat{\mathbf{Z}} $$&quot;,  is true, c.f. (MO-post) (because there can be non-trivial Artin-Schreier coverings). One way or another, the cited source only states it for algebraically closed fields of characteristic zero. Nurnochgeist (talk) 13:24, 12 September 2021 (UTC)