SMF

Modular forms and algebraic $K$-theory

Modular forms and algebraic $K$-theory

A. J. SCHOLL
  • Année : 1992
  • Tome : 209
  • Format : Papier, Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 11G40
  • Pages : 85-97
  • DOI : 10.24033/ast.156

This paper is a slightly expanded version of the talk given at the conference. We sketch an example of a non-trivial element of $K_2$ of a certain threefold, whose existence is related to the vanishing of an incomplete $L$-function of a modular form at $s = 1$. This is preceded with a simple account, for the non-specialist, of some of the conjectures (mostly due to Beilinson) which relate ranks of $K$-groups and orders of $L$-functions, supplemented by examples coming from modular forms.

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