The aim of this note is to give a friendly introduction to Arakelov geometry, starting with a modern reformulation of Minkowski’s geometry of numbers and arriving to the formulation of the arithmetic Grothendieck– Riemann–Roch theorem of Gillet–Soulé. In between, we motivate and explain the bases of arithmetic intersection theory.
Keywords
- Grothendieck–Riemann–Roch
- Arakelov geometry
- analytic torsion