I read Neukirch’s book “Algebraic Number Theory”, and its remark following to proposition VI.2.3, there is an assertion that natural map $\mathbb{A}\_K \otimes\_K L \to \mathbb{A}\_L$ is isomorphism. How can it be proved ?



base change of adele rings
This is Theorem 1 in Chapter IV-1 of Weil: Basic Number Theory. See also Corollaries 1-2 after the proof of this theorem.


