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This is a very soft question, and I'm not sure what I expect as an answer.

In SGA6, Expose XIII, Theoreme 5.1 it is proven that, if $X$ is a proper scheme over a field $k$, then $NS(X)$ is finitely generated. Here $NS(X) := \mathrm{Pic}_{X/k}(k)/\mathrm{Pic}_{X/k}^0(k)$.

However, on wikipedia's page for the "theorem of the base" this theorem is only stated for smooth projective varieties. In an earlier question on MO the same happens; see Modern Proof of the Theorem of the Base. A quick google search gives a lot of papers citing this result from SGA6, but most authors impose smoothness when citing SGA6. Do note that Section 5.3 in these notes math.stanford.edu/~conrad/249CS15Page/handouts/abvarnotes.pdf states that $NS(X)$ is finitely generated for proper geometrically integral, not necessarily smooth, schemes.

What is the reason that the theorem of the base from SGA6 is mostly cited for smooth proper schemes? Does the Neron-Severi group exhibit pathological behaviour if $X$ is singular?

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    $\begingroup$ There's no good reason, and in particular nothing pathological for the non-smooth case. Perhaps some paper working with smooth varieties stated the result in the relevant context and someone getting it from there copied the SGA6 reference without reading it and carried over the smoothness for safety, and then it spread due to people continuing to copy the citation from papers without reading the original reference. Near the end of 8.4 in the book Neron Models the result is stated in the same generality as in SGA6 (in particular, no parasitic smoothness hypotheses). $\endgroup$
    – nfdc23
    Feb 13 '18 at 2:05
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The comment by nfdc23 answers the question:

"There's no good reason, and in particular nothing pathological for the non-smooth case. Perhaps some paper working with smooth varieties stated the result in the relevant context and someone getting it from there copied the SGA6 reference without reading it and carried over the smoothness for safety, and then it spread due to people continuing to copy the citation from papers without reading the original reference. Near the end of 8.4 in the book Neron Models the result is stated in the same generality as in SGA6 (in particular, no parasitic smoothness hypotheses)."

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