Aspects of Iwasawa theory over function fields

  • Andrea Bandini

    Università degli Studi di Pisa, Italy
  • Francesc Bars

    Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain
  • Ignazio Longhi

    National Taiwan University, Taipei, Taiwan
Aspects of Iwasawa theory over function fields cover
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We consider -extensions of a global function field and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as well. When dealing with the Selmer group of an abelian variety defined over , we provide all the ingredients to formulate an Iwasawa Main Conjecture relating the Fitting ideal and the -adic -function associated to and . We do the same, with characteristic ideals and -adic -functions, in the case of class groups (using known results on characteristic ideals and Stickelberger elements for -extensions). The final section provides more details for the cyclotomic -extension arising from the torsion of the Carlitz module: in particular, we relate cyclotomic units with Bernoulli–Carlitz numbers by a Coates–Wiles homomorphism.