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Hi, everyone.

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

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    $\begingroup$ 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 $R$. $\endgroup$
    – Leo Alonso
    Commented Apr 29, 2013 at 14:20
  • $\begingroup$ I'm sure an answer can be very quickly found at math.stackexchange.com $\endgroup$
    – Olivier
    Commented Apr 29, 2013 at 14:21
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    $\begingroup$ The question is subtler than it appears, depending on the topology you choose its formal spectrum is completely different. $\endgroup$
    – Leo Alonso
    Commented Apr 29, 2013 at 14:27
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    $\begingroup$ I think there is no "natural" topology, as Leo says. $\endgroup$
    – Filippo Alberto Edoardo
    Commented Apr 29, 2013 at 15:39
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    $\begingroup$ discrete valuation ring I suppose, en.wikipedia.org/wiki/Discrete_valuation_ring $\endgroup$
    – Pietro Majer
    Commented Apr 29, 2013 at 19:52

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