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arXiv · 1406.0786

Uniformly Presented Vector Spaces

John D. Wiltshire-Gordon
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Abstract

Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only once the number of generators is fixed. We develop a theory of "uniformly presented vector spaces" to compute with these uniform families, introducing a formalism of finitely generated functors from the category of finite sets to the category of finite dimensional Q-vector spaces. We show that these representations have finite length and polynomial dimension away from the empty set, and produce finite leftward resolutions by manageable functors.

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John D. Wiltshire-Gordon. 2014-06-03. Uniformly Presented Vector Spaces. https://arxiv.org/abs/1406.0786

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