On the Categorical Entropy and the Topological Entropy
On the Categorical Entropy and the Topological Entropy
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关于分类熵和拓扑熵
DOI：
10.1093/imrn/rnx131
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发表时间：
2017
影响因子：
1
通讯作者：
Takahashi Atsushi
中科院分区：
文献类型：
--
作者：
Kikuta Kohei;Takahashi Atsushi
对于具有分裂生成器的三角范畴的精确endofunctor，熵的概念由Dimitrov-Haiden-Katzarkov-Kontsevich给出，它是实变量的（可能是负无穷）实值函数。在本文中，我们提出了一个猜想，该猜想自然地推广了 Gromov-Yomdin 定理，并表明光滑射影簇的满射自同态的分类熵等于其拓扑熵。此外，我们在充足的规范或反规范束的情况下计算派生类别的自等价熵。
To an exact endofunctor of a triangulated category with a split generator, the notion of entropy is given by Dimitrov–Haiden–Katzarkov–Kontsevich, which is a (possibly negative infinite) real-valued function of a real variable. In this article, we propose a conjecture which naturally generalizes the theorem by Gromov–Yomdin, and show that the categorical entropy of a surjective endomorphism of a smooth projective variety is equal to its topological entropy. Moreover, we compute the entropy of autoequivalences of the derived category in the case of the ample canonical or anti-canonical sheaf.