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23
Fermat’s Last Theorem
 Current Developments in Mathematics
, 1995
"... The authors would like to give special thanks to N. Boston, K. Buzzard, and B. Conrad for providing so much valuable feedback on earlier versions of this ..."
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Cited by 56 (10 self)
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The authors would like to give special thanks to N. Boston, K. Buzzard, and B. Conrad for providing so much valuable feedback on earlier versions of this
Deligne periods of mixed motives, Ktheory and the entropy of certain Z n actions
, 1997
"... this paper have been announced in [D3] where a short introduction to mixed motives can also be found. A much more thorough treatment of motives is given in [JKS]. For the Beilinson conjectures and related notions like Deligne cohomology we recommend the book [RSS]. Some observations of the present p ..."
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Cited by 50 (2 self)
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this paper have been announced in [D3] where a short introduction to mixed motives can also be found. A much more thorough treatment of motives is given in [JKS]. For the Beilinson conjectures and related notions like Deligne cohomology we recommend the book [RSS]. Some observations of the present paper may be of interest to researchers in other fields of mathematics than arithmetic geometry e.g. in dynamical systems. For this reason I have occasionally recalled standard material in the first two sections. It is a pleasure for me to thank Y. Ihara for the invitation to Kyoto and the RIMS for support. I would also like to thank D.W. Boyd for intersting correspondence and for bringing the above mentioned polynomial to my attention.
Computational Aspects of Curves of Genus at Least 2
 Algorithmic number theory. 5th international symposium. ANTSII
, 1996
"... . This survey discusses algorithms and explicit calculations for curves of genus at least 2 and their Jacobians, mainly over number fields and finite fields. Miscellaneous examples and a list of possible future projects are given at the end. 1. Introduction An enormous number of people have per ..."
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Cited by 14 (3 self)
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. This survey discusses algorithms and explicit calculations for curves of genus at least 2 and their Jacobians, mainly over number fields and finite fields. Miscellaneous examples and a list of possible future projects are given at the end. 1. Introduction An enormous number of people have performed an enormous number of computations on elliptic curves, as one can see from even a perfunctory glance at [29]. A few years ago, the same could not be said for curves of higher genus, even though the theory of such curves had been developed in detail. Now, however, polynomialtime algorithms and sometimes actual programs are available for solving a wide variety of problems associated with such curves. The genus 2 case especially is becoming accessible: in light of recent work, it seems reasonable to expect that within a few years, packages will be available for doing genus 2 computations analogous to the elliptic curve computations that are currently possible in PARI, MAGMA, SIMATH, apec...
Galois representations and modular forms
 Bull. Amer. Math. Soc
, 1995
"... Abstract. In this article, I discuss material which is related to the recent ..."
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Cited by 11 (0 self)
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Abstract. In this article, I discuss material which is related to the recent
A report on Wiles' Cambridge lectures
 APPEARED IN BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
, 1994
"... In lectures at the Newton Institute in June of 1993, Andrew Wiles announced a proof of a large part of the TaniyamaShimura Conjecture and, as a consequence, Fermat’s Last Theorem. This report for nonexperts discusses the mathematics involved in Wiles’ lectures, including the necessary background a ..."
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Cited by 5 (0 self)
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In lectures at the Newton Institute in June of 1993, Andrew Wiles announced a proof of a large part of the TaniyamaShimura Conjecture and, as a consequence, Fermat’s Last Theorem. This report for nonexperts discusses the mathematics involved in Wiles’ lectures, including the necessary background and the mathematical history.
On finiteness conjectures for modular quaternion algebras
 Math. Proc. Camb. Philos. Soc
"... Abstract. It is conjectured that there exist only finitely many isomorphism classes of endomorphism algebras of abelian varieties of bounded dimension over a fixed number field. We explore this conjecture when particularized to quaternion endomorphism algebras of abelian surfaces of GL2type over Q ..."
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Abstract. It is conjectured that there exist only finitely many isomorphism classes of endomorphism algebras of abelian varieties of bounded dimension over a fixed number field. We explore this conjecture when particularized to quaternion endomorphism algebras of abelian surfaces of GL2type over Q by giving a moduli interpretation which translates the question into the diophantine arithmetic of Shimura curves embedded in Hilbert surfaces. We address the resulting problems on these curves by local and global methods, including Chabauty techniques on explicit equations of Shimura curves. 1.
Galois theory, discriminants and torsion subgroup of elliptic curves
 JOURNAL OF PURE AND APPLIED ALGEBRA 214 (2010) 1340–1346
, 2010
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