Equivalences on program schemes

A program scheme may be informally described as a program with the interpretation (i.e., the meaning of the basic instructions or standard functions) left unspecified. This paper studies the equivalence of program schemes under different classes of interpretations, with emphasis on those in which the functions are permitted to be partial. Several different equivalence relations are defined, and their interrelationship and solvability examined both for the class of all program schemes, and for each subclass (n≥1) in which the number of registers is at most n

Motivic homotopy theory of group scheme actions

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.Comment: Final version, to appear in Journal of Topology. arXiv admin note: text overlap with arXiv:1403.191