The essential dimension of low dimensional tori via lattices

Case, Gareth and MacDonald, Mark (2019) The essential dimension of low dimensional tori via lattices. PhD thesis, Lancaster University.

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Abstract

The essential dimension, ed_k(G), of an algebraic group G is an invariant that measures the complexity of G-torsors over fields. The correspondence between algebraic tori and finite subgroups of GL_n(Z) means one can establish bounds on ed_k(T) of an algebraic torus T by studying the action of the corresponding subgroup of GL_n(Z).