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We provide a characterization of finite \'etale morphisms in tensortriangular geometry. They are precisely those functors which have aconservative right adjoint, satisfy Grothendieck--Neeman duality, and for whichthe relative dualizing object is trivial (via a canonically-defined map).more » « less
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Barthel, Tobias; Heard, Drew; Sanders, Beren (, The Quarterly Journal of Mathematics)Abstract We compare the homological support and tensor triangular support for ‘big’ objects in a rigidly-compactly generated tensor triangulated category. We prove that the comparison map from the homological spectrum to the tensor triangular spectrum is a bijection and that the two notions of support coincide whenever the category is stratified, extending the work of Balmer. Moreover, we clarify the relations between salient properties of support functions and exhibit counter-examples highlighting the differences between homological and tensor triangular support.more » « less
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Patchkoria, Irakli; Sanders, Beren; Wimmer, Christian (, Transactions of the American Mathematical Society)
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