Entropy in the category of perfect complexes with cohomology of finite length |
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Authors: | Mahdi Majidi-Zolbanin Nikita Miasnikov |
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Affiliation: | 1. Department of Mathematics, LaGuardia Community College of the City University of New York, 31-10 Thomson Avenue, Long Island City, NY 11101, United States of America;2. Department of Mathematical Sciences, State University of New York at Oswego, 7060 Route 104, Oswego, NY 13126, United States of America |
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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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Keywords: | 13B40 14B25 13B10 37P99 Entropy Triangulated categories Exact endofunctors Perfect complexes Flat extensions Additivity of entropy |
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