TY - JOUR
T1 - Monoidal infinity category of complexes from Tannakian viewpoint
AU - Fukuyama, Hiroshi
AU - Iwanari, Isamu
N1 - Funding Information:
I. Iwanari was supported by Japan Society for the Promotion of Science.
PY - 2013/6
Y1 - 2013/6
N2 - In this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable ∞-categories of quasi-coherent complexes. It can be viewed as a derived analogue of Tannaka duality. As a consequence, we deduce that an algebraic stack satisfying a certain condition can be recovered from the symmetric monoidal stable ∞-category of quasi-coherent complexes with tensor operation.
AB - In this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable ∞-categories of quasi-coherent complexes. It can be viewed as a derived analogue of Tannaka duality. As a consequence, we deduce that an algebraic stack satisfying a certain condition can be recovered from the symmetric monoidal stable ∞-category of quasi-coherent complexes with tensor operation.
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U2 - 10.1007/s00208-012-0843-8
DO - 10.1007/s00208-012-0843-8
M3 - Article
AN - SCOPUS:84877110388
SN - 0025-5831
VL - 356
SP - 519
EP - 553
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 2
ER -