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Cup product of $p$ first Galois Cohomologies of rationals, with coefficients in $\mu_{p}$

Let $p$ be an odd prime and $\mu_{p}$ be the group of $p^\text{th}$-roots of unity. Then, there exists a cup-product map which maps the product of $p$-copies of $H^{1}(\mathbb{Q}, \mu_{p})$ into $H^{p}...
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