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Motivic Serre invariants, ramification, and the analytic Milnor fiber

- J. Nicaise, J. Sebag
- Mathematics
- 5 January 2007

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 the… Expand

A trace formula for rigid varieties, and motivic Weil generating series for formal schemes

- J. Nicaise
- Mathematics
- 1 March 2007

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 show… Expand

Weight functions on non-archimedean analytic spaces and the Kontsevich-Soibelman skeleton

- M. Mustaţǎ, J. Nicaise
- Mathematics
- 27 December 2012

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 a… Expand

Néron Models and Base Change

- L. H. Halle, J. Nicaise
- Mathematics
- 25 September 2012

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 and… Expand

The essential skeleton of a degeneration of algebraic varieties

- J. Nicaise, Johannes Chenyang Xu
- Mathematics
- 15 July 2013

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 projective… Expand

Weight functions on Berkovich curves

- M. Baker, J. Nicaise
- Mathematics
- 3 June 2015

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 $C$. We… Expand

Formal and rigid geometry: an intuitive introduction, and some applications

- J. Nicaise
- Mathematics
- 19 January 2007

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

- J. Kollár, J. Nicaise, C. Y. Xu
- Mathematics
- 8 October 2015

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 while… Expand

Motivic zeta functions of degenerating Calabi–Yau varieties

- L. H. Halle, J. Nicaise
- Mathematics
- 31 January 2017

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 Galois… Expand

Motivic Serre invariants and Weil restriction

- J. Nicaise, J. Sebag
- Mathematics
- 15 February 2008

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 the… Expand

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