Nonexistence of negative weight derivations on graded Artin algebras: A conjecture of Halperin
S.~Halperin conjectured that if \(F\to E\to B\) is a fibration with simply connected base \(B\), and if the rational cohomology algebra of \(F\) is an Artin algebra of the form \(Q[x_{0},\ldots,x_{n}]/(f_{0},\ldots,f_{n})\), then the Serre spectral sequence for the fibration collapses. The conjecture can be stated algebraically in terms of the nonexistence of negative weight derivations on rings such as the one described above. Here, the conjecture is proven for \(n=2\).
scientific article; zbMATH DE number 1309245