Noncommutative Balmer spectra and structure of monoidal triangulated categories

Many settings in representation theory, algebraic geometry and mathematical physics lead to monoidal triangulated categories which are generally nonsymmetric. We will present a study of their noncommutative Balmer spectra, which includes a classification of all thick ideals and a generalized Carlson's connectedness theorem. The cohomological and Balmer support maps will be linked via a notion of categorical center of the cohomology ring of a monoidal triangulated category. This is a joint work with Dan Nakano and Kent Vashaw.

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