Algebraic Number Theory and Related Topics 2018. November 26-30, 2018. edited by Takao Yamazaki and Shuji Yamamoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.The goal of this manuscript is to provide a survey of good reduction criteria for hyperbolic polycurves. In particular, we give outlines of the proofs of the main theorems of the papers [19] and [20], which are details of the talk “Criteria for good reduction of hyperbolic polycurves” given at “Algebraic Number Theory and Related Topics 2018”. Also, this paper contains a proof of a specialization theorem of pro-L fundamental groups
