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Preprints, Working Papers, ... Year : 2008

Moduli of linear representations, symmetric products and the non commutative Hilbert scheme

Abstract

Let $k$ be a commutative ring and let $R$ be a commutative $k-$algebra. Let $A$ be a $R-$algebra. We discuss the connections between the coarse moduli space of the $n-$dimensional representations of $A,\,$ the non-commutative Hilbert scheme on $A$ and the affine scheme which represents multiplicative homogeneous polynomial laws of degree $n$ on $A$. We build a norm map which specializes to the Hilbert-Chow morphism on the geometric points when $A$ is commutative and $k$ is an algebraically closed field. This generalizes the construction done by Grothendieck, Deligne and others. When $k$ is an infinite field and $A=k\{x_1,\dots,x_m\}$ is the free $k-$associative algebra on $m$ letters, we give a simple description of this norm map.

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Dates and versions

hal-00441319 , version 1 (16-12-2009)

Identifiers

  • HAL Id : hal-00441319 , version 1

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Francesco Vaccarino. Moduli of linear representations, symmetric products and the non commutative Hilbert scheme. 2008. ⟨hal-00441319⟩
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