In Theorem VI.2, why did you restrict the degree of the polynomials? I am fairly certain that the same result will hold without the bound. ]]>

To be fair, the errors here are all mine; on MO, Rosen simply asserts

min\{\prod_{v\in P}|x|_v^{-1}:x\in S_A(n)\}=2^{O(n)},

which is true, if unexplained, and I’m simply trying (apparently unsuccessfully) to provide a slightly more rigorous explanation of why it’s true. I’ll take some time and try to get it sorted properly.

Hey, besides, it’s also a square root of -1.

]]>I don’t think that completely solves the problem. Not all algebraic numbers arise from root extensions. The classic example is a root of x^5 + x+1=0. The Galois group is of the polynomial is S_5 and one cannot represent any of the roots by any amount of simple root extractions.

]]>JZ #11: I’ve accidentally used the index ‘i’ twice — the intended meaning was the field of fractions of Z[\alpha_1,\alpha_2,…,\alpha_s], where any individual a_i might draw on more than one \alpha_j, not just a single \alpha_i.

I’ve posted an updated print at http://blog.rossry.net/static/qc_tameness.pdf and emailed it to Scott, so that he can update his link.

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