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Award ID contains: 2052936

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  1. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of Geometric Invariant Theory. We apply this to two familiar moduli problems: the stack of Λ-modules and the stack of pairs. In both examples, we construct a Θ-stratification of the stack, defined in terms of a polynomial numerical invariant, and we construct good moduli spaces for the open substacks of semistable points. One of the essential ingredients is the construction of higher-dimensional analogues of the affine Grassmannian for the moduli problems considered. 
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    Accepted Manuscript Full Text Available
  2. ; ; ; (, Forum of Mathematics, Sigma)
    We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of étale, smooth, or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove local structure theorems for stacks and their derived counterparts and the existence of henselizations along linearly fundamental closed substacks. These results establish the existence of Ferrand pushouts, which answers positively a question of Temkin-Tyomkin. 
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    Accepted Manuscript Full Text Available