Realizing algebraic invariants of hyperbolic surfaces

Jeon, BoGwang

doi:10.1090/tran/7271

Realizing algebraic invariants of hyperbolic surfaces
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by BoGwang Jeon PDF

Trans. Amer. Math. Soc. 371 (2019), 147-172 Request permission

Abstract:

Let $S_g$ ($g\geq 2$) be a closed surface of genus $g$. Let $K$ be any real number field, and let $A$ be any quaternion algebra over $K$ such that $A\otimes _K\mathbb {R}\cong M_2(\mathbb {R})$. We show that there exists a hyperbolic structure on $S_g$ such that $K$ and $A$ arise as its invariant trace field and invariant quaternion algebra.

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