Tropical and Non-Archimedean Geometry.

Intro -- Preface -- 1. Overview of the workshop -- 2. Tropical Geometry from a Non-Archimedean Viewpoint -- 3. Tropicalization and analytification -- Polyhedral structures on tropical varieties -- 1. Introduction -- 2. Gröbner complex -- 3. Proofs -- Acknowledgements -- References -- Lifting nonproper tropical intersections -- 1. Introduction -- 2. Analytifications and tropicalizations -- 3. Compatible and compactifying fans -- 4. The moving lemma -- 5. Continuity of intersection numbers -- 6. Tropical lifting theorems -- 7. An example -- References -- Fewnomial systems with many roots, and an Adelic Tau Conjecture -- 1. Introduction -- 2. Applications and new conjectures on straight-line programs -- 3. Background: from triangles to toric deformations and tropical varieties -- 4. Proving our main results -- 5. Wrapping up: Invariance of _{ }( , ), and the proofs of Proposition 1.4, Theorem 1.10, and Lemmata 4.1 and 4.2 -- Acknowledgements -- References -- Non-Archimedean Coamoebae -- Introduction -- 1. Tropicalization and coamoebae -- 2. Non-Archimedean coamoebae and phase tropical varieties -- 3. Coamoebae of tropically simple varieties -- References -- On the structure of non-archimedean analytic curves -- 1. Introduction -- 2. The skeleton of a generalized annulus -- 3. Semistable decompositions and skeleta of curves -- 4. Relation with semistable models -- 5. The metric structure on an analytic curve -- References -- Non-archimedean uniformization and monodromy pairing -- 1. Introduction -- 2. Notation -- 3. Monodromy pairing -- 4. Tate curves -- 5. Uniformization of abelian varieties -- 6. Uniformization of curves -- 7. Uniformization of Jacobian varieties -- 8. Arithmetic Schottky groups -- Acknowledgements -- References -- Diophantine geometry and analytic spaces -- 1. Introduction -- 2. The standard height function.

3. Heights for line bundles, canonical heights -- 4. Level sets for the canonical height -- 5. Equidistribution (arithmetic case) -- 6. Measures on analytic spaces -- 7. Bogomolov's conjecture for totally degenerate abelian varieties -- Acknowledgements -- References -- Tropicalizing vs. compactifying the Torelli morphism -- 1. Introduction -- 2. Moduli spaces of curves -- 3. Moduli spaces of abelian varieties -- 4. The Torelli maps -- 5. The anticontinuity of the reduction maps -- References -- Primer for the algebraic geometry of sandpiles -- 1. Introduction -- 2. Sandpiles -- 3. Lattice ideals -- 4. Toppling ideals -- 5. Gröbner bases of toppling ideals -- 6. Zeros of the toppling ideal -- 7. Resolutions -- 8. Gorenstein toppling ideals -- References.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.