Grothendieck and Verdier introduced the notion of triangulated category to extract homological informations. This structure appear in many branches of Mathematics. Balmer introduced the notion of spectrum of tensor triangulated category as classifying support data. This opens a way for geometric study of theses abstract categorical data. Balmer also defined the structure sheaf on this spectrum and as an application reconstructed large class of schemes from the category of perfect complexes associated with them. In this talk we’ll recall Balmer’s construction of spectrum and its application to reconstruction problem. We’ll also discuss computation of Balmer spectrum for some other tensor triangulated categories obtained in a joint work with Vivek Mallick.

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