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Aug 12, 2022 at 14:40 comment added Sergey Guminov @WillSawin You are absolutely right! It really is only defined for quasi-finite morphisms (Definition 2.2.7). It looks like otherwise $f_{!*}$ is well-defined, but there are problems with a lot of its desired good properties. Could you just type it up as an answer?
Aug 12, 2022 at 13:23 comment added Will Sawin Is $f_{!*}$ defined outside the quasifinite context? That might be the only problem.
Aug 12, 2022 at 9:59 history asked Sergey Guminov CC BY-SA 4.0