ScalingStacks

6.6 [0373]

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6.6

Let T∈Dp,q​(W)T\in D_{p,q}(W) and ω∈Ar,s​(W)\omega\in A^{r,s}(W) for an open subset WW of Xan{X^{\rm an}}. Then we define T∧ω∈Dp−r,q−s​(W)T\wedge\omega\in D_{p-r,q-s}(W) by (T∧ω)​(α)=T⁡(ω∧α)(T\wedge\omega)(\alpha)=T(\omega\wedge\alpha) for α∈Acp−r,q−s​(W)\alpha\in A_{c}^{p-r,q-s}(W). Since the wedge product with a given form is a continuous operation on Ac​(W)A_{c}(W), it is clear that T∧ωT\wedge\omega is really a current on WW.

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