We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic K-theory is representable in the resulting homotopy category. Additionally, we establish homotopical purity and blow-up theorems for finite abelian groups.
Motivic homotopy theory of group scheme actions / J. Heller, A. Krishna, P.A. Oestvaer. - In: JOURNAL OF TOPOLOGY. - ISSN 1753-8416. - 8:4(2015), pp. 1202-1236. [10.1112/jtopol/jtv030]
Motivic homotopy theory of group scheme actions
P.A. Oestvaer
2015
Abstract
We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic K-theory is representable in the resulting homotopy category. Additionally, we establish homotopical purity and blow-up theorems for finite abelian groups.
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