Abstract

We generalize a result due to Bloch on the prorepresentability of Milnor $K$-cohomology groups at the identity. In particular, we prove, for $X$ a smooth, proper, and geometrically connected variety defined over an algebraic field extension  $k∕\mathbb{Q}$, that the functor

defined on Artin local $k$-algebras $(A,{\mathfrak{𝔪}}_A)$ with $A∕{\mathfrak{𝔪}}_A\cong <!--FUNCTION\; APPLICATION-->k$, is prorepresentable provided that certain Hodge numbers of $X$ vanish.

Keywords

Mathematical Subject Classification

Milestones

Authors