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arXiv · 1401.6685

Higher-dimensional study of extensions via torsors

Cristiana Bertolin·Ahmet Emin Tatar
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Abstract

Let S 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 of abelian sheaves on S.

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Cristiana Bertolin, Ahmet Emin Tatar. 2014-01-26. Higher-dimensional study of extensions via torsors. https://doi.org/10.1007/s10231-017-0686-8

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