Dear everyone,


(i) Who is the father of the adjective “syntomic” in algebraic geometry?


(ii) And why did he choose to introduce a new term for what we already know from EGA IV.19.3.6 and SGA 6.VIII.1.1 as “flat, locally of finite presentation, and local complete intersection”? 


Thanks!



Why “syntomic” if “flat, locally of finite presentation, and local complete intersection” is already available?
Mazur gives the following beautiful justification, which explains the “syn-” in “syntomic” as well.



> 
> Dear Thanos,
> 
> 
> Thanks for your question. I'm thinking of “ local complete
>  intersection” as being a way of cutting out a (sub-) space from an
>  ambient surrounding space; the fact that it is flat over the parameter
>  space means that each such "cutting" as you move along the parameter
>  space, is---more or less---cut out similarly. I'm also thinking of the
>  word "syntomic" as built from the verb temnein (i.e., to cut) and the
>  prefix "syn" which I take in the sense of "same" or "together". So I
>  think it fits.
> 
> 
> Best wishes,
> 
> 
> Barry
> 
> 
> 


