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Potential minor error in paper-qcoh.tex: "ring ℚ of integers".

Open finegeometer opened this issue 1 year ago • 1 comments

Hi!

paper-qcoh.tex, on lines 1318 and 1319, contains the phrase "and~$A$ is the ring~$\QQ$ of integers". While I admit I'm not fully understanding everything, this seems likely to be an error. Isn't ℤ the integers, and ℚ the rationals?

Sincerely, A random reader.


Surrounding context:

\begin{rem}The finite presentability condition in
Lemma~\ref{lemma:fp-double-dual} cannot be dropped. For instance, in the case
that~$\TT$ is the theory of commutative rings with unit and~$A$ is the
ring~$\QQ$ of integers, we have~$\Spec(A^\sim) \cong \Spec(0^\sim)$, where~$0$
is the zero ring, as~$\QQ$ allows ring homomorphisms only in those finitely
presented rings in which~$1 = 0$ holds. Hence~$A^\sim$
and~$(U_\TT)^{\Spec(A^\sim)} \cong (U_\TT)^{\Spec(0^\sim)} \cong 0^\sim$ do not coincide.
\end{rem}

In the rendered pdf, this appears as Remark 4.12, on page 17.

finegeometer avatar Jun 29 '23 03:06 finegeometer

Oh! Good catch! Thank you for your careful reading and for letting me know. :-)

The correct counterexample is the ring of rationals, not the ring of integers. I will fix that immediately.

With which name can I list you in the acknowledgments of the paper? :-)

iblech avatar Jun 29 '23 13:06 iblech