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Zbl 1236.11058
Howe, Everett W.; Nart, Enric; Ritzenthaler, Christophe
Jacobians in isogeny classes of abelian surfaces over finite fields. (English)
[J] Ann. Inst. Fourier 59, No. 1, 239-289 (2009). ISSN 0373-0956; ISSN 1777-5310/e

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.
[Robert Guralnick (Los Angeles)]

MSC 2000:: *11G20 Curves over finite and local fields
11G25 Varieties over finite and local fields
14G10 Zeta-functions and related questions
14G15 Finite ground fields

Keywords: curve; Jacobian; abelian surface; zeta function; Weil polynomial; Weil number

Cited in: Zbl 1197.14028 Zbl 1166.11020

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