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,,x_m ]is the free k-associative algebra on m letters, we give a simple description of this norm map
Moduli of linear representations, symmetric products and the non commutative Hilbert scheme in Geometric Methods in Representation Theory, II Michel Brion Editor Séminaires et Congrès 24-II (2012) / Vaccarino, Francesco. - STAMPA. - 2:(2012), pp. 435-456. (Intervento presentato al convegno Geometric methods in representation theory' tenutosi a Grenoble nel 16 June -4 July, 2008).
Moduli of linear representations, symmetric products and the non commutative Hilbert scheme in Geometric Methods in Representation Theory, II Michel Brion Editor Séminaires et Congrès 24-II (2012)
VACCARINO, FRANCESCO
2012
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,,x_m ]is the free k-associative algebra on m letters, we give a simple description of this norm mapPubblicazioni consigliate
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https://hdl.handle.net/11583/2379902
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