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Autor(en): 
  • Vladimir G. Berkovich
  • Integration of One-Forms on P-Adic Analytic Spaces. (Am-162) 
     

    (Buch)
    Dieser Artikel gilt, aufgrund seiner Grösse, beim Versand als 2 Artikel!


    Übersicht
     
    Lieferstatus:   i.d.R. innert 14-24 Tagen versandfertig
    Veröffentlichung:  2007  
    Genre:  Schulbücher 
    ISBN:  9780691128627 
    EAN-Code: 
    9780691128627 
    Verlag:  Princeton Univ Pr 
    Einband:  Kartoniert  
    Sprache:  English  
    Dimensionen:  H 234 mm / B 162 mm / D 12 mm 
    Gewicht:  268 gr 
    Seiten:  168 
    Bewertung: Titel bewerten / Meinung schreiben
    Inhalt:
    Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties.

    This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path.

    Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry.

      
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