The Frobenius exponent of Cartier subalgebras

Abstract

Let $R$ be a standard graded finitely generated algebra over an $F$-finite field of prime characteristic, localized at its maximal homogeneous ideal. In this note, we prove that that Frobenius complexity of $R$ is finite. Moreover, we extend this result to Cartier subalgebras of $R$.

9 pages, accepted for publication in the Journal of Pure and Applied Algebra