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Formal Structures and Representation Spaces

โœ Scribed by Lieven Le Bruyn; Geert Van de Weyer

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
170 KB
Volume
247
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

M. Kapranov introduced and studied in math.AG/9802041 the noncommutative formal structure of a smooth affine variety. In this note we show that his construction is a particular case of micro-localization and extend the construction functorially to representation schemes of affine algebras. We describe explicitly the formal completions in the case of path algebras of quivers and initiate the study of their finite dimensional representations.

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When computing on a (generally) uncountable topological structure d, such as the topological field of real numbers R, one must by necessity compute on a set of concrete approximations P for d. One way to do this is to represent the original structure d using P in such a way that computations on P tr