Dynamics on Berkovich Spaces in Low Dimensions

By Mattias Jonsson. 2012

114 citations recorded by the source corpus.

These are expanded lecture notes for the summer school on Berkovich spaces that took place at the Institut de Mathematiques de Jussieu, Paris, during June 28–July 9, 2010. They serve to illustrate some techniques and results from the dynamics on low-dimensional Berkovich spaces and to exhibit the structure of these spaces.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/741d091dbc29284fbac04d8385903cf1b74a3b4c

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In Mathematical Physics

1. Mattias Jonsson
2. S. Boucksom
3. M. Mustaţă
4. Chi Li
5. H. Blum
6. Robert J. Berman
7. C. Favre
8. Yuchen Liu

Citations in the corpus

• Valuations and asymptotic invariants for sequences of ideals (2010, background): “A function on VX,ξ is psh if and only if it satisfies certain convexity conditions [19, 2, 42, 28].”
• An algebraic approach to the openness conjecture of Demailly and Kollár (2012, background): “ng v(m x) = 1, where m x is the maximal ideal. One can equip Vwith a natural topology in which it is compact Hausdor; it also has the structure of a tree and is studied in detail in [FJ04] (see also [Jon12]). To a psh germ at xone can associate a lower semicontinuous function on Vwhose minimum is eq”
• A non-Archimedean approach to K-stability (2018, background): “This means v can be viewed as a point in the valuative tree V = Vξ at ξ, see [FJ04] and also [Jon12].”