Halperin conjecture

In mathematics, more specifically in rational homotopy theory, the Halperin conjecture concerns the rational Serre spectral sequence of certain fibrations. It is named after the Canadian mathematician Stephen Halperin.
The statement.
Suppose that formula_1 is a fibration of simply connected spaces such that formula_2 is rationally elliptic and formula_3 (i.e., formula_2 has non-zero Euler characteristic), then the Serre spectral sequence associated to the fibration collapses at the formula_5 page.
The status of the conjecture.
As of 2019, Halperin's conjecture is still open. Gregory Lupton has reformulated the conjecture in terms of formality relations.