In 1942 he graduated from the Scuola Normale Superiore in Pisa, and became assistant professor Francesco Severi at the University of Rome in 1946.
In 1961 he was recalled to Pisa as a teacher first of Geometry, then of Algebra.
From 1968 to his death he taught Geometry at the University of Padua.
Iacopo was a visiting scholar at the Institute for Advanced Study in 1982.
In p-adic Hodge theory, so-called period rings are denoted by the letter B, a nod to Barsotti’s work.