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3 results

  • An additive variant of Somekawa's K-groups and Kähler differentials

  • Toshiro Hiranouchi
  • Journal:
    Journal of K-Theory / Volume 13 / Issue 3 / June 2014
    Published online by Cambridge University Press:
    20 March 2014, pp. 481-516
    Print publication:
    June 2014

  • We introduce a Milnor type K-group associated to commutative algebraic groups over a perfect field. It is an additive variant of Somekawa's K-group. We show that the K-group associated to the additive group and q multiplicative groups of a field is isomorphic to the space of absolute Kähler differentials of degree q of the field, thus giving us a geometric interpretation of the space of absolute Kähler differentials. We also show that the K-group associated to the additive group and Jacobian variety of a curve is isomorphic to the homology group of a certain complex.

  • Differential Forms and Smoothness of Quotients by Reductive Groups

  • Guillaume Jamet
  • Journal:
    Compositio Mathematica / Volume 133 / Issue 2 / September 2002
    Published online by Cambridge University Press:
    04 December 2007, pp. 151-171
    Print publication:
    September 2002
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  • Let π : X [xlarr ] Y be a good quotient of a smooth variety X by a reductive algebraic group G and 1[les ]k≤ dim (Y) an integer. We prove that if, locally, any invariant horizontal differential k-form on X (resp. any regular differential k-form on Y) is a Kähler differential form on Y then codim(Ysing)>k+1. We also prove that the dualizing sheaf on Y is the sheaf of invariant horizontal dim(Y)-forms.

  • Galois Theory of BdR+

  • ADRIAN IOVITA, ALEXANDRU ZAHARESCU
  • Journal:
    Compositio Mathematica / Volume 117 / Issue 1 / May 1999
    Published online by Cambridge University Press:
    04 December 2007, pp. 1-33
    Print publication:
    May 1999
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  • We formulate and prove necessary and sufficient conditions for the Galois correspondence to hold for the ring of p-adic periods B+dR.