Arithmetic properties of algebraic curves from a pseudo-characteristic polynomial of a finite potent endomorphism

Abstract The aim of this work is to offer the definition and the main properties of a pseudo-characteristic polynomial of a finite potent endomorphism. From this polynomial we can characterize the spectrum of a bounded finite potent linear operator on a Hilbert space and we study arithmetic properties of complete algebraic curves. In particular, we provide a new algebraic proof of the Residue Theorem.