2014/05/27 by Quy Thuong Lê, Le Quy Thuong, Thuong, Le Quy
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #math.AG #math.LO
paper · pdf · doi:10.48550/arxiv.1405.7065
21 pages
arxiv created 2014/05/27 · openalex publication_date 2014/05/27 · arxiv updated 2014/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Thanks to Hrushovski-Loeser's work on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom-Sebastiani theorem in the case of regular functions. Moreover, slightly extending of Hrushovski-Loeser's construction adjusted to Sebag, Loeser and Nicaise's motivic integration for formal schemes and rigid varieties, we formulate and prove an analogous result for formal functions. The latter is meaningful as it has been a crucial element of constructing Kontsevich-Soibelman's theory of motivic Donaldson-Thomas invariants.