Tensor Triangular Geometry - Lecture 1

Explore tensor triangular geometry in this 58-minute lecture by Greg Stevenson at the Hausdorff Center for Mathematics. Delve into the analogy between symmetric monoidal triangulated categories and rings, discovering how this perspective provides an equivalent to affine algebraic geometry. Learn about constructing spectra for essentially small symmetric monoidal triangulated categories, examining their properties and various examples. Investigate the challenges of extending the theory to compactly generated settings and analyze the limitations of the analogy between tensor triangular and algebraic geometry. Examine the tensor triangulated analogue of fields, their role in understanding localizations, and the complexities involved in constructing residue fields at spectral points. This lecture is part of the HIM Summer School series on "Spectral methods in algebra, geometry, and topology."