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Reading about the calculation of the Brauer group of rational numbers, the calculations of the group are extremely lengthy and technical. First of all, it will be very helpful to me if someone can explicitly give me a class which corresponds to a nontrivial member of the Brauer group of rational numbers. Secondly, I appreciate it if someone can sketch the calculation if we assume we know the Brauer group of every local field is $\mathbb{Q} \backslash \mathbb{Z}$.

Reading about the calculation of the Brauer group of rational numbers, the calculations of the group are extremely lengthy and technical. First of all, it will be very helpful to me if someone can explicitly give me a class which corresponds to a nontrivial member of the Brauer group of rational numbers. Secondly, I appreciate it if someone can sketch the calculation if we assume we know the Brauer group of every local field is $\mathbb{Q}/\mathbb{Z}$.

Reading about the calculation of the Brauer group of rational numbers, the calculations of the group are extremely lengthy and technical. First of all, it will be very helpful to me if someone can explicitly give me a class which corresponds to a nontrivial member of the Brauer group of rational numbers. Secondly, I appreciate it if someone can sketch the calculation if we assume we know the Brauer group of every local field is $\mathbb{Q} \ \mathbb{Z}$.

Reading about the calculation of the Brauer group of rational numbers, the calculations of the group are extremely lengthy and technical. First of all, it will be very helpful to me if someone can explicitly give me a class which corresponds to a nontrivial member of the Brauer group of rational numbers. Secondly, I appreciate it if someone can sketch the calculation if we assume we know the Brauer group of every local field is $\mathbb{Q} \backslash \mathbb{Z}$.

Reading about the calculation of the Brauer group of rational numbers, the calculations of the group are extremely lengthy and technical. First of all, it will be very helpful to me if someone can explicitly give me a class which corresponds to a nontrivial member of the Brauer group of rational numbers. Secondly, I appreciate it if someone can sketch the calculation if we assume we know the Brauer group of every local field is $\mathbb{Z}$.

Reading about the calculation of the Brauer group of rational numbers, the calculations of the group are extremely lengthy and technical. First of all, it will be very helpful to me if someone can explicitly give me a class which corresponds to a nontrivial member of the Brauer group of rational numbers. Secondly, I appreciate it if someone can sketch the calculation if we assume we know the Brauer group of every local field is $\mathbb{Q} \ \mathbb{Z}$.