Smith Colloquium

October 11, 2018

Shizhang Li, Columbia University

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