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Entropy in the category of perfect complexes with cohomology of finite length. (arXiv:1601.01064v2 [math.AC] UPDATED)
来源于:arXiv
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. 查看全文>>