Arinkin, DmitroGaitsgory, Dennis2019-09-302017-05-08Arinkin, D., and D. Gaitsgory. 2018. The Category of Singularities as a Crystal and Global Springer Fibers. Journal of the American Mathematical Society 31: 135-214.0894-03471088-6834http://nrs.harvard.edu/urn-3:HUL.InstRepos:41426696We prove the "gluing conjecture" on the spectral side of the categorical geometric Langlands conjecture. The key tool is the structure of crystal on the category of singularities, which allows one to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.en-USJournal Article2019-09-3010.1090/jams/882