This is an announcement for the paper “The positive polynomial Schur property in Banach lattices” by Geraldo Botelho<https://arxiv.org/search/math?searchtype=author&query=Botelho%2C+G>, José Lucas P. Luiz<https://arxiv.org/search/math?searchtype=author&query=Luiz%2C+J+L+P>. Abstract: We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$-spaces are shown to be positively polynomially Schur, lattice analogues of results on Banach spaces are obtained and relationships with the positive Schur and the weak Dunford-Pettis properties are established. https://arxiv.org/abs/2003.11626