Entropy in the category of perfect complexes with cohomology of finite length
arXiv:1601.01064 · doi:10.1016/j.jpaa.2018.09.008
Abstract
Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to category-theoretical entropy. The two entropies are shown to be equal when the ring is regular, and also for the Frobenius endomorphism of a complete local ring of positive characteristic. Furthermore, given a flat morphism of Cohen-Macaulay local rings endowed with compatible endomorphisms of finite length, it is shown that local entropy is "additive". Finally, over a ring that is a homomorphic image of a regular local ring, a formula for local entropy in terms of an asymptotic partial Euler characteristic is given.
Final version, published in Journal of Pure and Applied Algebra. This version also includes arXiv:1404.1541 [math.AC]