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Sep 2, 2019 at 7:06 history bounty ended Yoël
Aug 31, 2019 at 15:51 comment added Yoël I meant, the formal completion of $\underline{\mathrm{U}}_V$ at $v$. But I think it's clear anyway :-)
Aug 31, 2019 at 15:28 comment added Yoël Thank you GTA for your answer ! I'm trying to figure out the details, can you please elaborate a bit on what you mean by "Seeing fibers as formal completions" ? Do you mean that the functor obtained by base change from $\mathcal{O}^S_F$-algebras to $(\mathcal{O}_F^S)_v$-algebras is represented by the formal completion of $(\underline{\mathrm{U}}_V)_v$ ?
Aug 31, 2019 at 3:22 history answered GTA CC BY-SA 4.0