Can paper burn without oxygen or air?
No, the paper will not burn without oxygen being present.

Paper is made primarily of cellulose which is a polymer of glucose.



If you heat paper in a vacuum the cellulose simply decomposes to $\ce{H2O}$, $\ce{CO2}$, $\ce{CO}$ and carbon.  As the paper decomposes it will "char" or turn brown to black as the cellulose polymer degrades.  Here is a link to an abstract describing the process in more detail.