Roland Lötscher: Essential dimension and canonical dimension of gerbes banded by groups of multiplicative type

Submission: 2013, Sep 24

We prove the formula ed(X)=cdim(X)+ed(A) for any gerbe X banded by an algebraic group A which is the kernel of a homomorphism of algebraic tori Q->S with Q invertible and S split. This result is applied to prove new results on the essential dimension of algebraic groups.

2010 Mathematics Subject Classification: 20G15, 14A20, 11E72

Keywords and Phrases: essential dimension, canonical dimension, algebraic stack, gerbe, group of multiplicative type

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