The Williams conjecture is false for irreducible subshifts.
Kim, K.H., Roush, F.W. (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Kim, K.H., Roush, F.W. (1997)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Abramovich, Dan, Voloch, Jose Felipe (1996)
The New York Journal of Mathematics [electronic only]
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Nils Bruin, E. Victor Flynn, Damiano Testa (2014)
Acta Arithmetica
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We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.
Fabio Bardelli, Gian Pietro Pirola (1989)
Inventiones mathematicae
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D. Gieseker (1982)
Inventiones mathematicae
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Abel Castorena (2005)
Bollettino dell'Unione Matematica Italiana
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In the moduli space of curves of genus , , let be the locus of curves that do not satisfy the Gieseker-Petri theorem. In the genus seven case we show that is a divisor in .
Joe Harris (1980)
Mathematische Annalen
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Alexandru Buium, José Felipe Voloch (1996)
Compositio Mathematica
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Nitaj, Abderrahmane (1993)
Experimental Mathematics
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Nguyen Van Chau (2011)
Annales Polonici Mathematici
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In certain cases the invertibility of a polynomial map F = (P,Q): ℂ²→ ℂ² can be characterized by the irreducibility and the rationality of the curves aP+bQ = 0, (a:b) ∈ ℙ¹.
Lomont, Chris (2002)
Experimental Mathematics
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Dan Abramovich, Joe Harris (1991)
Compositio Mathematica
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