Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hi, everyone.

Let $A$ be a complete DVR with uniformizer $t$, $R:=A[[X]]$. What is the natural topology of $R$ ?

share|improve this question
1  
The ring $R$ is complete both for the $\langle X \rangle$-adic topology and for the $\langle t, X \rangle$-adic topology. So it depends on what you want to study about $R$. –  Leo Alonso Apr 29 '13 at 14:20
    
I'm sure an answer can be very quickly found at math.stackexchange.com –  Olivier Apr 29 '13 at 14:21
4  
The question is subtler than it appears, depending on the topology you choose its formal spectrum is completely different. –  Leo Alonso Apr 29 '13 at 14:27
1  
I think there is no "natural" topology, as Leo says. –  Filippo Alberto Edoardo Apr 29 '13 at 15:39
1  
discrete valuation ring I suppose, en.wikipedia.org/wiki/Discrete_valuation_ring –  Pietro Majer Apr 29 '13 at 19:52

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.