*Title*: **On rigid varieties with projective reduction**

*Abstract*: Bosch, Lütkebohmert and Raynaud laid down the foundations
relating formal and rigid geometry. The type of questions they treat are mostly
concerned with going from the rigid side to formal side. In the past, I considered
the opposite type of question, namely to what extent properties on the formal
side inform us about rigid geometry. More precisely, we will see what geometric
consequences one can deduce under the assumption that the rigid space has a
projective reduction.
In this talk, I shall first say some background of rigid geometry and Ray-
naud's theory of formal models along with some examples. Then I will state the
main theorem and a corollary. If time permitted, I will say something about
the proof.

Smith Colloquium Spring 2018