Anisotropy, biased pairings, and the Lefschetz property for pseudomanifolds and cycles

We prove the hard Lefschetz property for pseudomanifolds and cycles in any characteristic with respect to an appropriate Artinian reduction. The proof is a combination of Adiprasito's biased pairing theory and a generalization of a formula of Papadakis-Petrotou to arbitrary characteristic. In particular, we prove the Lefschetz theorem for doubly Cohen Macaulay complexes, solving a generalization of the g-conjecture due to Stanley. We also provide a simplified presentation of the characteristic 2 case, and generalize it to pseudomanifolds and cycles.