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Higher-dimensional study of extensions via torsors

Author:
Bertolin, Cristiana  Tatar, Ahmet Emin  


Journal:
ANNALI DI MATEMATICA PURA ED APPLICATA


Issue Date:
2018


Abstract(summary):

Let be a site. First we define the 3-category of torsors under a Picard S-2-stack and we compute its homotopy groups. Using calculus of fractions, we define also a pure algebraic analogue of the 3-category of torsors under a Picard S-2-stack. Then we describe extensions of Picard S-2-stacks as torsors endowed with a group law on the fibers. As a consequence of such a description, we show that any Picard S-2-stack admits a canonical free partial left resolution that we compute explicitly. Moreover, we get an explicit right resolution of the 3-category of extensions of Picard S-2-stacks in terms of 3-categories of torsors. Using the homological interpretation of Picard S-2-stacks, we rewrite this three categorical dimensions higher right resolution in the derived category D(S) of abelian sheaves on S.


Page:
433---468


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