Scott Balchin- The Local-to-Global Principle

Explore the concept of the local-to-global principle in rigidly-compactly generated tensor-triangulated categories in this 51-minute lecture by Scott Balchin at the Hausdorff Center for Mathematics. Delve into the recent work of Barthel-Heard-Sanders, which builds upon Benson-Iyengar-Krause's research, providing a general framework for stratification. Examine the necessary and sufficient conditions for classifying localising tensor ideals using arbitrary subsets of the Balmer spectrum. Investigate how the local-to-global principle allows for the reconstruction of arbitrary objects from pieces supported at individual Balmer primes. Learn about ongoing research with Stevenson, focusing on the use of pointless topology of the Balmer spectrum to determine whether a category satisfies the local-to-global principle. Cover key topics including motivation, big objects, subspaces, local and global aspects, local categories, scattered spaces, and sublocals.