Talk:Direct image with compact support

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What is the relationship between this proper direct image ${\displaystyle f_{!}}$ with the K-theory one: ${\displaystyle f_{!}{\mathcal {F}}=\sum _{i=0}^{n}(-1)^{i}R^{i}f_{*}{\mathcal {F}}}$ are these two f_! somehow related or they are just two different things using the same symbol? 155.198.157.118 (talk) 10:31, 28 July 2008 (UTC)[reply]