Geometry of Numbers

Mathematics – Algebraic Geometry

Scientific paper

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A paper by Tsukasa Hayashi is added

Scientific paper

We develop a global cohomology theory for number fields by offering
topological cohomology groups, an arithmetical duality, a Riemann-Roch type
theorem, and two types of vanishing theorem. As applications, we study moduli
spaces of semi-stable lattices, and introduce non-abelian zeta functions for
number fields.

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