Motivic classes of some classifying stacks

• We prove that the class of the classifying stack BPGL(n) is the multiplicative inverse of the class of the projective linear group PGL(n) in the Grothendieck ring of stacks K-0(Stack(k)) for n = 2 and n = 3 under mild conditions on the base field k. In particular, although it is known that the multiplicativity relation {T} = {S} . {PGL(n)} does not hold for all PGL(n)-torsors T -> S, it holds for the universal PGL(n)-torsors for said n.

Ämnesord

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

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Mathematics

matematik

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