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One quiver to rule them all

Lieven Le Bruyn
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Abstract

To a formally smooth algebra A we associate a quiver setting (Q,a) containing enough information to reconstruct all the local quiver settings determining the etale local structure of finite dimensional representation schemes of A, see math.AG/9904171. Conjecturally, in a (yet to be developed) non-commutative etale topology, A is locally isomorphic to an algebra B which in turn is Morita equivalent (via the dimension vector a) to the path algebra CQ of the quiver Q.

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Lieven Le Bruyn. 2003-04-15. One quiver to rule them all. https://arxiv.org/abs/math/0304196

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