[1][2][3] Abramovich received a bachelor's degree at Tel Aviv University in 1987 and completed a doctorate at Harvard University in 1991 under Joe Harris (Subvarieties of abelian varieties and of Jacobians of curves).

[5] Among other topics, he has dealt with birational geometry, the resolution of singularities, subvarieties of abelian varieties, limits for the torsion of elliptic curves, rational and integer points on algebraic varieties and moduli spaces of vector bundles on curves.

Together with Felipe Voloch, in 1992 he succeeded in making progress toward proving the Mordell-Lang Conjecture in characteristic p (the full proof came later from Ehud Hrushovski).

He has been a guest scholar at, among other institutions, the Hebrew University of Jerusalem, the Max Planck Institute for Mathematics in Bonn, the Mathematical Sciences Research Institute (MSRI), the Pierre and Marie Curie University in Paris and at IHES.

He was an invited speaker at the 2018 International Congress of Mathematicians ("Resolution of singularities of complex algebraic varieties and their families").