Actions of abelian $p$-groups on smooth projective varieties

In my talk, I will discuss the bound on the rank of an abelian $p$-group acting faithfully on a smooth $K$-scheme, where $K$ is an algebraically closed field of characteristic different from $p$. This result was established in the work of J. Kollár and Z. Zhuang. The proof relies on methods from equivariant characteristic class theory, which will also be briefly outlined in the talk.