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J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1)Summer School 2017 - Arakelov Geometry and diophantine applications


Description : In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of sections of V is the non-negative real number h0θ(E,∥.∥):=log∑v∈Ee−π∥v∥2. In these lectures, I will firstly discuss diverse properties of the invariant h0θ and of its extensions to certain infinite dimensional generalizations of Euclidean lattices. Then I will present applications of this formalism to transcendence theory and to algebraization theorems in Diophantine geometry.
Contributor : Fanny Bastien <>
Submitted on : Friday, February 23, 2018 - 11:13:52 AM
Last modification on : Friday, March 30, 2018 - 3:22:08 PM