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Jacobians in isogeny classes of abelian surfaces over finite fields. (English) Zbl 1236.11058
This well written paper provides a complete classification as to which quartic polynomials occur as the characteristic polynomial of Frobenius on the Jacobian of a genus 2 curve over a finite field. This builds on earlier work of several authors. The main cases handled in this paper are split isogeny classes and supersingular isogeny classes.

MSC:
11G20 Curves over finite and local fields
11G25 Varieties over finite and local fields
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14G15 Finite ground fields in algebraic geometry
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