The Stacks project

Exercise 111.48.3. Let $X$ be a ringed space. Define cup-product maps

\[ \mathop{\mathrm{Ext}}\nolimits ^ i_ X(\mathcal{G}, \mathcal{H}) \times \mathop{\mathrm{Ext}}\nolimits ^ j_ X(\mathcal{F}, \mathcal{G}) \longrightarrow \mathop{\mathrm{Ext}}\nolimits ^{i + j}_ X(\mathcal{F}, \mathcal{H}) \]

for $\mathcal{O}_ X$-modules $\mathcal{F}, \mathcal{G}, \mathcal{H}$. (Hint: this is a super general thing.)

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View Exercise 111.48.3 as pdf