Talk:Direct image with compact support

What is the relationship between this proper direct image $$f_!$$ with the K-theory one: $$f_! \mathcal{F} = \sum_{i=0}^n (-1)^i R^i f_* \mathcal{F}$$ 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)