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The Riemann–Roch Theorem in Arakelov Geometry

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Part of the Progress in Mathematics book series (PM,volume 321)

Abstract

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

Mathematics Subject Classification (2010). Primary 14C40; Secondary 14G40

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Correspondence to Gerard Freixas i Montplet .

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Montplet, G.F.i. (2017). The Riemann–Roch Theorem in Arakelov Geometry. In: Mourtada, H., Sarıoğlu, C., Soulé, C., Zeytin, A. (eds) Algebraic Geometry and Number Theory . Progress in Mathematics, vol 321. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-47779-4_4

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