Algebraic Geometry And Arithmetic Curves Qing Liu Pdf -

– Applies the general theory to birational geometry and intersection theory on arithmetic surfaces. It culminates in the study of reduction of algebraic curves and the fundamental theorem of stable reduction by Deligne-Mumford. Amazon.com Key Features

, it serves as a rigorous alternative or companion to classic texts like Hartshorne, with a specific focus on the geometry of arithmetic surfaces. Overview of Content algebraic geometry and arithmetic curves qing liu pdf

Advanced topics like sheaves of differentials, Grothendieck's duality theory, and the Riemann-Roch theorem for projective curves. – Applies the general theory to birational geometry

: Develops intersection theory specifically for arithmetic surfaces. Grothendieck's duality theory