Higher rank Nichols algebras of diagonal type with finite arithmetic root system in positive characteristic

The classification of finite dimensional Nichols algebras is a key part of the lifting method by N. Andruskiewitsch and H.-J. Schneider for finite dimensional pointed Hopf algebras. In this paper, we classify all rank $r\ge 5$ Nichols algebras of diagonal type with finite irreducible root systems over fields of positive characteristic. Using Weyl groupoids, arithmetic root systems, and Cartan graphs, we show that such Nichols algebras correspond exactly to the generalized Dynkin diagrams listed in Table 1.