Abstract
In this paper we define and study triangulated categories in which the Hom-spaces have Krull dimension at most one over some base ring (hence they have a natural 2-step filtration), and each factor of the filtration satisfies some Calabi–Yau type property.
If
Dedicated to Yuji Yoshino on the occasion of his 60th birthday.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 24340004
Award Identifier / Grant number: 23540045
Award Identifier / Grant number: 20244001
Award Identifier / Grant number: 22224001
Funding source: Engineering and Physical Sciences Research Council
Award Identifier / Grant number: EP/K021400/1
Funding statement: The first author was partially supported by JSPS Grant-in-Aid for Scientific Research 24340004, 23540045, 20244001 and 22224001, and the second author by EPSRC under grant EP/K021400/1.
Acknowledgements
The authors would like to thank Hailong Dao for many interesting discussions regarding this work, especially with regards to the class group calculation in Section 5.2.
References
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