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What is known about the Brauer Group of a Nodal curve (complete integral curve) over $k$ with singularity as ordinary double point?

Is it trivial if $k$ algebraically closed?

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  • $\begingroup$ Isn't it obvious from the smooth case? If you have an Azumaya algebra on the normalization, you can make it into an algebra on the singular curve by gluing together its values at particular points. The gluing data is an element of $PGL_n$. If you trivialize the algebra as the endomorphisms of a vector bundle, then all you have to do to trivialize its descent is lift from $PGL_n$ to $GL_n$. $\endgroup$
    – Will Sawin
    Commented Jul 13, 2019 at 14:05
  • $\begingroup$ @Will Sawin thanks for reply. I have got the result in Grothendieck Paper $\endgroup$
    – PSUN
    Commented Jul 14, 2019 at 14:52

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