Milnor K-groups and function fields of hypersurfaces in positive characteristic

2012/02/29 by Scully, Stephen
#13N05 #19D45 #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1202.6604

Abstract

Let X be an integral affine or projective hypersurface over a field F of characteristic p>0, and let F(X) denote its function field. In a recent article, Dolphin and Hoffmann obtained an explicit description of the kernel of the natural restriction homomorphism between the rings of absolute Kähler differentials of F and F(X), respectively. In this note, we examine the possibility of deriving an analogous result for mod-p Milnor K-theory using the Bloch-Gabber-Kato theorem.

Related

• Milnor K₂ and field homomorphisms
• Reconstructing function fields from Milnor K-theory
• Invitation to higher local fields, Part I, section 2: p-primary part of the Milnor K-groups and Galois cohomology of fields of characteristic p
• Invariant hypersurfaces for derivations in positive characteristic
• Kato-Kuzumaki's properties for function fields over higher local fields