2018/01/12 by Lucian M. Ionescu, Ionescu, Lucian M. · 1 citation
Computer Science · Mathematics · Pharmacology, Toxicology and Pharmaceutics · #11Sxx #14F40 #16E40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Number Theory (math.NT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1801.07570
openalex publication_date 2018/01/12 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
Presenting p-adic numbers as em deformations of finite fields allows a\nbetter understanding of Frobenius lifts and their connection with p-derivations\nin the sense of Buium citeBuium-Main. In this way "numbers em are\nfunctions", as recognized before citeManin:Numbers, allowing to view initial\nstructure deformation problems as arithmetic differential equations as in\n citeBuium-Manin, and providing a cohomological interpretation to Buium\ncalculus via Hochschild cohomology which controls deformations of algebraic\nstructures.\n Applications to p-adic periods are considered, including to the classical\nEuler gamma and beta functions and their p-adic analogues, from a cohomological\npoint of view.\n Connections between various methods for computing scattering amplitudes are\nrelated to the moduli space problem and period domains.\n