Arithmetic, Geometry, Cryptography and Coding Theory: by Gilles Lachaud, Christophe Ritzenthaler, Michael A. Tsfasman PDF

By Gilles Lachaud, Christophe Ritzenthaler, Michael A. Tsfasman

ISBN-10: 0821847163

ISBN-13: 9780821847169

This quantity includes the lawsuits of the eleventh convention on AGC2T, held in Marseilles, France in November 2007. There are 12 unique study articles overlaying asymptotic homes of worldwide fields, mathematics homes of curves and better dimensional types, and functions to codes and cryptography. This quantity additionally includes a survey article on functions of finite fields by way of J.-P. Serre. AGC2T meetings occur in Marseilles, France each 2 years. those overseas meetings were a huge occasion within the zone of utilized mathematics geometry for greater than twenty years

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Additional resources for Arithmetic, Geometry, Cryptography and Coding Theory: International Conference November 5-9, 2007 Cirm, Marseilles, France

Sample text

The Weierstraß points of C are mapped onto E[2] and hence to the ramification points of π : E → P1 . By our hypothesis, three of the Weierstraß points lie over the zero-point of E whose image in P1 (K) is denoted by P4 . The three others are mapped one-to-one to the points of order 2 of E. , P3 the images of these points. The discriminant divisor of f is the conorm (or pullback) of a divisor of P1 with support equal to one point P5 ∈ P1 (K). , P5 }. 4. Let f0 : C → E be a minimal genus 2 cover of odd degree n of an elliptic curve E/K.

B. Leep and L. M. 172] , we deduce the following result. 1. Let Q1 and Q2 be two quadrics in P4 (Fq ) with w(Q1 , Q2 ) = 5. Then, |Q1 ∩ Q2 | ≤ 3q 2 + q + 1. 172] the hypothesis on the order of the two quadrics Q1 and Q2 is too restrictive and does not work in the general case. Let us recall another property, free from this condition. 2. 70-71 ] Let Q1 and Q2 be two quadrics in Pn (Fq ) and l an integer such that 1 ≤ l ≤ n−1. e. , xn−l ) and |Q1 ∩ Q2 ∩ En−l (Fq )| ≤ m. Then |Q1 ∩ Q2 | ≤ mq l + πl−1 .

Consequently, the cones meet in exactly 2q + 1, 3q + 1 and 4q + 1. Secondly two hyperbolic quadrics in P3 (Fq ) can also intersect in exactly three lines (two lines in a regulus and the third in the complementary regulus). 8 and table 3 above, we deduce the following table 4. Let us explain the table 4. For type 1, the intersection of a hyperbolic quadric and a cone quadric, contains at most two lines; therefore 3q and 2q + 1 are respectively the maximum number of this intersection when containing (exactly or) at most two lines or exactly one line.

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Arithmetic, Geometry, Cryptography and Coding Theory: International Conference November 5-9, 2007 Cirm, Marseilles, France by Gilles Lachaud, Christophe Ritzenthaler, Michael A. Tsfasman

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