# Tag Info

## New answers tagged local-rings

1 vote

### Depth of almost complete intersection rings

In general, depth can be zero. Let me give an example. Let $X\subset\mathbb{P}^n$ be a smooth variety of dimension $d$ which is subcanonical (this means $K_X=O_X(*)$ for some integer $*$) and NOT ...
• 5,712
Yes, it is consistent, it even follows from the Kock-Lawvere axiom, as follows. We defined $\mathrm{Spf}(R[[\epsilon]]) := \mathrm{colim}_n \mathrm{Spec}(R[\epsilon]/(\epsilon^n))$, so we have R^{\...