ScalingStacks

\propname 4.4.5 . [01S6]

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\propname 4.4.5.

Soit φ:Y/L→X/k\varphi\colon Y/L\rightarrow X/k un morphisme d’espaces analytiques qui est topologiquement propre. Supposons que Y/LY/L soit purement de dimension dd. On a défini des courants φ∗​δY∈𝒟d,d​(X)\varphi_{*}\delta_{Y}\in\mathscr{D}_{d,d}(X) et φ∗​δY∈𝒟d−1,d​(X)\varphi_{*}\delta_{Y}\in\mathscr{D}_{d-1,d}(X). On a la relation

d′⁡(φ∗​δY)=−φ∗​δ∂Ydans 𝒟d−1,d​(X).\mathop{\mathrm{d^{\prime}}}(\varphi_{*}\delta_{Y})=-\varphi_{*}\delta_{\partial Y}\qquad\text{dans $\mathscr{D}_{d-1,d}(X)$.} (4.4.5.1)

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