Titlebook: Arithmetic and Geometry; Papers Dedicated to Michael Artin,John Tate Book 1983 Springer Science+Business Media New York 1983 Multiplicatio

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Zeta-Functions of Varieties Over Finite Fields at s=1,Let . be a finite field of cardinality . = ... Let.be a fixed algebraic closure of .. Let . be a smooth projective algebraic variety of dimension . over . such that.is connected.

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The Torelli Theorem for Ordinary K3 Surfaces over Finite Fields,Shafarevich’s and Piatetski-Shapiro’s proof of the Torelli theorem for K3 surfaces over C [13] is one of the most beautiful proofs in complex algebraic geometry.

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https://doi.org/10.1007/978-1-4757-9284-3Multiplication; arithmetic; automorphic forms; automorphism; cohomology; polynomial; torsion

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Fracture Toughness Correlations,al point) is finitely generated. His proof was somewhat indirect. In 1928 Weil [5] in his thesis generalized Mordell’s result to abelian varieties of any dimension and to any algebraic number field as ground field. At the same time, Weil [6] gave a very simple and elegant proof of Mordell’s original

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Linear Elastic Fracture Mechanics,as worked on the arithmetic of elliptic curves is acutely aware, it is still dominated today, despite its long and rich history, by a wealth of tantilizing conjectures, which are convincingly supported by numerical evidence. The most important amongst these conjectures, at least from the point of vi