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Motivic Serre invariants, ramification, and the analytic Milnor fiber
We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce theExpand
A trace formula for rigid varieties, and motivic Weil generating series for formal schemes
We establish a trace formula for rigid varieties X over a complete discretely valued field, which relates the set of unramified points on X to the Galois action on its étale cohomology. Next, we showExpand
Weight functions on non-archimedean analytic spaces and the Kontsevich-Soibelman skeleton
We associate a weight function to pairs consisting of a smooth and proper variety X over a complete discretely valued field and a differential form on X of maximal degree. This weight function is aExpand
Néron Models and Base Change
Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 Introduction.- Preliminaries.- Models of curves and the Neron component series of a Jacobian.- Component groups andExpand
The essential skeleton of a degeneration of algebraic varieties
In this paper, we explore the connections between the Minimal Model Program and the theory of Berkovich spaces. Let $k$ be a field of characteristic zero and let $X$ be a smooth and projectiveExpand
Weight functions on Berkovich curves
Let $C$ be a curve over a complete discretely valued field $K$. We give tropical descriptions of the weight function attached to a pluricanonical form on $C$ and the essential skeleton of $C$. WeExpand
Formal and rigid geometry: an intuitive introduction, and some applications
We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory,Expand
Semi-stable extensions over 1-dimensional bases
Given a family of Calabi–Yau varieties over the punctured disc or over the field of Laurent series, we show that, after a finite base change, the family can be extended across the origin whileExpand
Motivic zeta functions of degenerating Calabi–Yau varieties
We study motivic zeta functions of degenerating families of Calabi–Yau varieties. Our main result says that they satisfy an analog of Igusa’s monodromy conjecture if the family has a so-called GaloisExpand
Motivic Serre invariants and Weil restriction
We study the interactions between Weil restriction for formal schemes and rigid varieties, Greenberg schemes, and motivic Serre invariants, and their behavior with respect to finite extensions of theExpand