cofiber - Weblio 英和・和英辞典 (original) (raw)
- Template:invoke:time, Grigory Garkusha, Alexander Neshitov, Ivan Panin, “Framed motives of relative motivic spheres”, in arXiv[1]:
The aim of this paper is to prove the following results stated in [GP1]: for any k {\displaystyle k} -smooth scheme X {\displaystyle X} and any n ≥ 1 {\displaystyle n\geq 1} the map of simplicial pointed sheaves ( − , A 1 ⌋ G m ) + ∧ n → T n {\displaystyle (-,\mathbb {A} ^{1}\rfloor \mathbb {G} _{m})_{+}^{\wedge n}\to T^{n}} induces a Nisnevich local level weak equivalence of S 1 {\displaystyle S^{1}} -spectra $ M f r ( X × ( A 1 ⌋ G m ) ∧ n ) → M f r ( X × T n ) {\displaystyle \$M_{fr}(X\times (\mathbb {A} ^{1}\rfloor \mathbb {G} _{m})^{\wedge n})\to M_{fr}(X\times T^{n})} a n d t h e s e q u e n c e o f {\displaystyle andthesequenceof} S^1 − s p e c t r a {\displaystyle -spectra} M f r ( X × T n × G m ) → M f r ( X × T n × A 1 ) → M f r ( X × T n + 1 ) {\displaystyle M_{fr}(X\times T^{n}\times \mathbb {G} _{m})\to M_{fr}(X\times T^{n}\times \mathbb {A} ^{1})\to M_{fr}(X\times T^{n+1})} $ is locally a homotopy cofiber sequence in the Nisnevich topology..