대수기하학
In 1979, Hartshorne was awarded the Leroy P. Steele Prize for "his expository research article Equivalence relations on algebraic cycles and subvarieties of small codimension, Proceedings of Symposia in Pure Mathematics, volume 29, American Mathematical Society, 1975, pp. 129-164; and his book Algebraic geometry, Springer-Verlag, Berlin and New York, 1977." In 2012, Hartshorne became a fellow of the American Mathematical Society.