A finiteness criterion for 2-dimensional representations of surface groups.

Abstract: Let C be a a complex algebraic curve of genus \geq 1, and let pi be its fundamental group. Let \rho: pi\rightarrow \GL_2(\C) be a semisimple 2-dimensional representation, such that \rho(\alpha) has finite order for every simple closed loop \alpha. We will prove that \rho has finite image. If time permits, we will mention applications of this result to the Grothendieck-Katz p-curvature conjecture. This is joint work with Anand Patel and Junho Peter Whang.

algebraic geometrynumber theory

Audience: researchers in the topic

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