my @to_keep = qw{ a c };
my %keepers;
foreach ( @to_keep ) {
    $keepers{$_}++;
}
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... I thought I could do the same thing using map ...

The way to do that with map would be like this:

my %keepers = map { $_ => 1 } @to_keep;
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The point is that, in this case, you want each iteration in map to return a key/value pair, not just a single value, and the "fat comma" (=>) does that for you.