MINIMA AND SLOPES OF RIGID ADELIC SPACES

Minima et pentes des espaces adéliques rigides

Eric Gaudron (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

This is a lecture for the Summer School "Arakelov Geometry and diophantine applications" (Institut Fourier, Grenoble, June 2017). We present an abstract of the theory of rigid adelic spaces over an algebraic extension of Q, developed in a previous article with G. Rémond (2017). We define the Harder-Narasimhan filtration, the slopes and several type of minima associated to such spaces. This formalism generalizes the Minkowski geometry of numbers for ellipsoids, the twisted height theory by Roy and Thunder as well as the slope theory of Hermitian vector bundles by Bost.

Mots clés: Adelic space; Rigid adelic space; Successive minima; Arakelov slopes; Twisted height; Arakelov degree; Harder-Narasimhan filtration; Hermite constant; Transference theorems

Domaines: Théorie des nombres [math.NT]

Eric Gaudron. MINIMA AND SLOPES OF RIGID ADELIC SPACES. Gaël Rémond; Emmanuel Peyre. Arakelov Geometry and diophantine applications, In press. ⟨hal-02445064v1⟩