Structured chain complexes IV (Ex)
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(Created page with "<wikitex>; Let $C$ be a bounded chain complex over a ring $R$. Show that for large enough $k$ we have $$ W_{\%}(\Sigma^k C) \simeq 0. $$ </wikitex> == References == {{#RefList...") |
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− | Let $C$ be a bounded chain complex over a ring $R$. Show that | + | Let $C$ be a bounded chain complex over a ring $R$. Show that we have |
− | $$ W_{\%}(\Sigma^k C) \simeq 0. $$ | + | $$ \mathrm{hocolim}_{k \rightarrow \infty} \Sigma^{-k} W_{\%}(\Sigma^k C) \simeq 0. $$ |
</wikitex> | </wikitex> | ||
− | == References == | + | == References== |
{{#RefList:}} | {{#RefList:}} | ||
[[Category:Exercises]] | [[Category:Exercises]] | ||
[[Category:Exercises without solution]] | [[Category:Exercises without solution]] |
Latest revision as of 12:29, 23 August 2013
Let be a bounded chain complex over a ring . Show that we have