Ramification in the cohomology of algebraic surfaces arising from ordinary double point singularities

Abstract

Let K be a field complete with respect to a discrete valuation whose residue field is algebraically closed of an odd positive characteristic. We study the ramification in the cohomology of a smooth proper surface X defined over K, under the assumption that X admits an integral model X whose special fibre has at worst ordinary double points. We will introduce a numerical invariant of X, in terms of which the ramification in the cohomology of X is determined.