Timeline for Reference for Hensel's Lemma in Algebraic Geometry

6 events

when toggle format	what		by	license	comment
Jan 6, 2017 at 21:10	vote	accept	thierry stulemeijer
Jan 6, 2017 at 21:09	answer	added	thierry stulemeijer		timeline score: 1
Mar 30, 2016 at 0:39	comment	added	nfdc23		Yes, though the reader doesn't need to be told about the reference 5.1.8 in EGA I (even though Grothendieck felt the need to mention it in that IV$_4$ 18.5 discussion).
Mar 29, 2016 at 8:38	comment	added	thierry stulemeijer		Indeed, thanks very much ! In order to be able to use 18.5.4(b), I just have to mention that since ($\text{Spec}(R)$,$\text{Spec}(R/\mathfrak{m})$) is a henselian couple, so is ($\text{Spec}(R)$,$\text{Spec}(R/\mathfrak{m}^k)$). As mentioned below 18.5.5, this is a direct consequence of Definition 18.5.5 and of $[EGA_{I}]$, 5.1.8.
Mar 29, 2016 at 3:28	comment	added	nfdc23		Since it suffices to treat $\ell = \infty$ (that doesn't need to be explained to the reader), you could say that the same proof applies verbatim upon making just one change: replace the reference to 18.5.11(b) with a reference to 18.5.4(b) (taking $S$ to be ${\rm{Spec}}(R)$ and $S_0$ to be ${\rm{Spec}}(R/\mathfrak{m}^k)$ in the notation of 18.5.4).
Mar 28, 2016 at 22:07	history	asked	thierry stulemeijer	CC BY-SA 3.0