江湖郎中
发表于 2025-3-26 21:59:57
Diophantus of Alexandria,metic over the field of rational numbers. It was 1,300 years before Western mathematicians became interested in this type of problem (Bombelli, Viète, Bachet, Fermat), … on reading Diophantus to be precise. He also introduced new methods and a special symbol to express an unknown, which makes him an essential precursor of algebraic notation.
urethritis
发表于 2025-3-27 02:52:05
Algebraic Closure; Affine Space,his is why they can quite easily be interpreted in terms of algebraic geometry, by adding if necessary rudiments of Galois theory. In this chapter, we introduce the algebraic and geometric concepts that seem best adapted to the arithmetic context.
女上瘾
发表于 2025-3-27 07:51:52
Projective Varieties; Conics and Quadrics,king in a projective setting. Arithmetic properties of projective varieties are strongly dependent on their geometry. The case of conics serves as a first illustration. Then we shall prove Springer’s and Brumer’s theorems on algebraic points on quadrics and intersections of quadrics.
受辱
发表于 2025-3-27 10:44:31
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财产
发表于 2025-3-27 14:33:13
Euclidean Rings,al to be interested in Euclid’s division algorithm too, which has given rise to some impressive works. On formalizing the notion of the ., unexpected algorithms, revealed by new methods, have recently been discovered. There are also connections to several old unsolved conjectures.
allergy
发表于 2025-3-27 21:42:43
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残暴
发表于 2025-3-27 22:34:49
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CLOWN
发表于 2025-3-28 05:31:31
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Brocas-Area
发表于 2025-3-28 07:46:23
-Adic Completions,The field of .-adic numbers was introduced by Hensel at the beginning of the twentieth century. This remarkable idea greatly simplifies computations involving congruences, and is also of considerable theoretical interest, preparing the way for powerful generalizations.
Fibrillation
发表于 2025-3-28 10:46:28
The Hasse Principle,The . asks the natural question: if a polynomial equation has non-trivial solutions in . and in .. for every prime ., can one deduce that it also has solutions in .? For quadratic forms, the answer is encouraging, but for more general situations this is only a “principle”, which may be verified or not.