Gregory's Server
https://api.semanticscholar.org/ is easier for this purpose: https://api.semanticscholar.org/graph/v1/paper/10.1002/pds.5070?fields=title,abstract
But where's the fun in that! Also, it doesn't include all abstracts, although it has some that CrossRef doesn't (e. g. some medical ones, which they probably get from PubMed)
Whoa!
curl -LH "Accept:application/json" https://dx.doi.org/10.1145/3356903 | jq .abstract
Sadly, some articles are missing abstracts here as well.
One more fun thing is that it can produce BibTeX:
curl -LH "Accept: text/bibliography; style=bibtex" http://dx.doi.org/10.1038/nrd842