vector bundle, 2-vector bundle, (∞,1)-vector bundle
real, complex/holomorphic, quaternionic
The concept of line n-bundle in algebraic geometry, classified by maps into the -fold delooping of the multiplicative group.
for , classified by the group of units;
for these are algebraic line bundles, classified by Picard group, modulated by Picard stack;
for these are algebraic line 2-bundles, classified by Brauer group, modulated by Brauer stack
According to (Grothendieck 64, prop. 1.4) for a Noetherian scheme whose local rings have strict Henselisations that are factorial (…explain…) then the cohomology groups
are all torsion groups for . (For this is the Brauer group.) See also this MO discussion.
See also at Friedlander-Milnor isomorphism conjecture.
Alexander Grothendieck, Torsion homologique et sections rationnelles, Séminaire Claude Chevalley, 3 (1958), Exp. No. 5, 29 p. (Numdam)
Alexander Grothendieck, Le groupe de Brauer : II. Théories cohomologiques. Séminaire Bourbaki, 9 (1964-1966), Exp. No. 297, 21 p. (Numdam)
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