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arXiv · 1601.01064

Entropy in the category of perfect complexes with cohomology of finite length

Mahdi Majidi-Zolbanin·Nikita Miasnikov
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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.

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BibTeXRIS

Mahdi Majidi-Zolbanin, Nikita Miasnikov. 2016-01-06. Entropy in the category of perfect complexes with cohomology of finite length. https://doi.org/10.1016/j.jpaa.2018.09.008

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