Donovan's conjecture on Morita finiteness of blocks with a given defect group

Field paper, Theorem 1.1: for each prime $p$, algebraically closed $K$ of characteristic $p$ and bound $M$, blocks of finite groups over $K$ with defect groups of order at most $M$ represent only finitely many $K$-linear Morita classes; defect groups may be nonabelian and $p=2$ is included. Integral companion, Theorem 1.1 and Corollary: the same over $W(\overline{\mathbb F}_p)$ and over each fixed complete DVR of characteristic zero with algebraically closed residue field, ramified included. Consequences: bounded Cartan entries and Loewy lengths. Not shown: explicit lists or bounds on the number of classes, or Morita finiteness over coefficient fields that are not algebraically closed.

Field paper, Theorem 1.1: for each prime $p$, algebraically closed $K$ of characteristic $p$ and bound $M$, blocks of finite groups over $K$ with defect groups of order at most $M$ represent only finitely many $K$-linear Morita classes; defect groups may be nonabelian and $p=2$ is included. Integral companion, Theorem 1.1 and Corollary: the same over $W(\overline{\mathbb F}_p)$ and over each fixed complete DVR of characteristic zero with algebraically closed residue field, ramified included. Consequences: bounded Cartan entries and Loewy lengths. Not shown: explicit lists or bounds on the number of classes, or Morita finiteness over coefficient fields that are not algebraically closed.