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Felix
Felix
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I am sorry, but I am quite new to Ext groups of sheaves. However, I have a closed embedding of projective $\mathbb{C}$-schemes $\iota : X \hookrightarrow Y$ and was wondering if $$\iota_*:\mathrm{Ext}^*_X(\mathcal{F},\mathcal{G}) \to \mathrm{Ext}^*_Y (\iota_*\mathcal{F},\iota_*\mathcal{G})$$ was an iso, respectively if there are certain properties of that map that I may exploit to control said map.

I am sorry, but I am quite new to Ext groups of sheaves. However, I have closed embedding of projective $\mathbb{C}$-schemes $\iota : X \hookrightarrow Y$ and was wondering if $$\iota_*:\mathrm{Ext}^*_X(\mathcal{F},\mathcal{G}) \to \mathrm{Ext}^*_Y (\iota_*\mathcal{F},\iota_*\mathcal{G})$$ was an iso, respectively if there are certain properties of that map that I may exploit to control said map.

I am sorry, but I am quite new to Ext groups of sheaves. However, I have a closed embedding of projective $\mathbb{C}$-schemes $\iota : X \hookrightarrow Y$ and was wondering if $$\iota_*:\mathrm{Ext}^*_X(\mathcal{F},\mathcal{G}) \to \mathrm{Ext}^*_Y (\iota_*\mathcal{F},\iota_*\mathcal{G})$$ was an iso, respectively if there are certain properties of that map that I may exploit to control said map.

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Felix
Felix
  • 213
  • 1
  • 6

is the induced map of an embedding an Iso on Ext-groups?

I am sorry, but I am quite new to Ext groups of sheaves. However, I have closed embedding of projective $\mathbb{C}$-schemes $\iota : X \hookrightarrow Y$ and was wondering if $$\iota_*:\mathrm{Ext}^*_X(\mathcal{F},\mathcal{G}) \to \mathrm{Ext}^*_Y (\iota_*\mathcal{F},\iota_*\mathcal{G})$$ was an iso, respectively if there are certain properties of that map that I may exploit to control said map.