11
votes
Accepted
Original proof of Hilbert irreducibility theorem
See Hilbert's Proof of His Irreducibility Theorem by Mark B. Villarino, Bill Gasarch, and Kenneth Regan. (Also available as an arXiv preprint.)
3
votes
Accepted
Isn't every algebraic operad equipped with a trivial weight?
The comment of Tom Goodwillie is correct. In the book, a connected weight graded operad is one that decomposes as:
$$\mathcal{P} = \mathbb{K} \mathrm{id} \oplus \mathcal{P}^{(1)} \oplus \mathcal{P}^{(...
1
vote
Accepted
Shrinking the base field of an affine variety
A standard reference is Chapter 6 of "Neron Models" of Bosch, Lütkebohmert and Raynaud, Springer, 1990. The original Grothendieck's exposés in the Cartan Seminar (1960--1961) are available ...
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