MINIMA AND SLOPES OF RIGID ADELIC SPACES

Abstract : 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.
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Submitted on : Monday, February 10, 2020 - 10:39:33 AM
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Eric Gaudron. MINIMA AND SLOPES OF RIGID ADELIC SPACES. Gaël Rémond; Emmanuel Peyre. Arakelov Geometry and diophantine applications, In press. ⟨hal-02445064v2⟩

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