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

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Majidi-Zolbanin, Mandi¹  Miasnikov, Nikita² 

[1] CUNY, LaGuardia Community Coll, Dept Math, 31-10 Thomson Ave, Long Isl City, NY 11101 USA

[2] SUNY Coll Oswego, Dept Math Sci, 7060 Route 104, Oswego, NY 13126 USA

关键词: Entropy;    Triangulated categories;    Exact endofunctors;    Perfect complexes;    Flat extensions;    Additivity of entropy;   

DOI  :  10.1016/j.jpaa.2018.09.008

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free