The aim of this paper is to prove the following results stated in [GP1]: for any k-smooth scheme X and any n#92;geq 1 the map of simplicial pointed sheaves (-,#92;mathbbA¹#92;rfloor#92;mathbbG#95;m)#123;#92;wedgen#125;#95;#43;#92;toTⁿ induces a Nisnevich local level weak equivalence of S¹-spectra $M#95;#123;fr#125;(X#92;times(#92;mathbbA¹#92;rfloor#92;mathbbG#95;m)#123;#92;wedgen#125;)#92;toM#95;#123;fr#125;(X#92;timesTⁿ)andthesequenceofS^1-spectraM#95;#123;fr#125;(X#92;timesTⁿ#92;times#92;mathbbG#95;m)#92;toM#95;#123;fr#125;(X#92;timesTⁿ#92;times#92;mathbbA¹)#92;toM#95;#123;fr#125;(X#92;timesT#123;n#43;1#125;)$ is locally a homotopy cofiber sequence in the Nisnevich topology..
Source: wiktionary