Mathematical Research Letters

Volume 22 (2015)

Number 2

On the character varieties of finitely generated groups

Pages: 579 – 604

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n2.a12

Author

Igor A. Rapinchuk (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Abstract

We establish three results dealing with the character varieties of finitely generated groups. The first two are concerned with the behavior of $\varkappa(\Gamma, n) = \dim X_n(\Gamma)$ as a function of $n$, and the third addresses the problem of realizing a $\mathbb{Q}$-defined complex affine algebraic variety as a character variety.

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