Title: Picard categories, determinant functors and K-theory
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Abstract: I will exhibit connections between:
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1) The Knudsen-Mumford theorem on the existence of a unique determinant functor
from bounded complexes to invertible sheaves.
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2) Deligne's Picard category of virtual objects of an exact category, which
models the 1-truncation of its K-theory spectrum.
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3) The Gillet-Waldhausen isomorphism between the K-theories of an exact category
and its category of bounded complexes.
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If time allows I will also show connections with:
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4) Determinant functors on triangulated categories with a "triangulated category
of true triangles", as suggested by Grothendieck.
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5) Maltsiniotis's conjecture on the agreement between the K-theories of an exact
category and its triangulated derivator.