Timeline for Question on localization technique

6 events

when toggle format	what		by	license	comment
Dec 4, 2012 at 18:37	history	edited	Fred Rohrer	CC BY-SA 3.0	edited body
Dec 4, 2012 at 16:57	vote	accept	Axy
Dec 4, 2012 at 15:26	comment	added	Fred Rohrer		... If the result holds in case we have a local base ring then it holds in this situation, and thus the claim will be proven once we prove it for the case of a local base ring.
Dec 4, 2012 at 15:25	comment	added	Fred Rohrer		Dear @Axy, concerning scalar restriction you should take a look at Bourbaki's Algèbre II.1.13. Concerning the proof, I explained that if $M_{\mathfrak{p}}=N_{\mathfrak{p}}$ for every prime ideal $\mathfrak{p}$ in $R_0$, then $M=N$. So, if we want to show that $M=N$, then we have to show that $M_{\mathfrak{p}}=N_{\mathfrak{p}}$ for every prime ideal $\mathfrak{p}$ in $R_0$. To do this, we take such a prime ideal and localise everything at it, obtaining a similar situation as before but this time over a local base ring...
Dec 4, 2012 at 14:56	comment	added	Axy		@Fred Rohrer: Dear Fred, what do you mean by the $B$ modules obtain from $M$ and $N$ by scalar restriction along $h$ are equal ? can you make it more precise? As you said we can conclude that $M_{\mathfrak_{p}}=N_{\mathfrak{p}}$ on $R_0$ and therefore $M=N$ on $R_0$. So, why prooving the problem in the local case makes the proof complete ?
Dec 4, 2012 at 13:35	history	answered	Fred Rohrer	CC BY-SA 3.0