CIMPA research school in Ho Chi Minh city in 2016

CIMPA research school on

Lattices and applications to cryptography and coding theory
Saigon University, Ho Chi Minh City, Vietnam.
August 1^st - 12^th, 2016

Lattices and Number theory
Lecturers: Peter Stevenhagen (Leiden) - Tran Nguyen Thanh Ha (Tor Vergata)

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Program

Number fields and their ring of integers, absolute values. Ramification index and residue class degree. Discriminant and ramification. Dirichlet Unit Theorem and Minkowski's theorem. Euclidean rings.

Arakelov divisor: definition and examples. Construction of the Arakelov class group. Hermitian line bundles and ideal lattices. Construction of the bijection between the Arakelov class group and the set of isometry class of ideal lattices.

Reduced Arakelov divisors. Finiteness of the set of reduced Arakelov divisor. Description of Buchmann's algorithm for computing the class number and the regulator of a number field in terms of the Arakelov class group and the set of reduced Arakelov divisor.