Displaying similar documents to “Successive minima on arithmetic varieties”

Diophantine approximation on algebraic varieties

Michael Nakamaye (1999)

Journal de théorie des nombres de Bordeaux

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We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.

An arithmetic analogue of Clifford's theorem

Richard P. Groenewegen (2001)

Journal de théorie des nombres de Bordeaux

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Number fields can be viewed as analogues of curves over fields. Here we use metrized line bundles as analogues of divisors on curves. Van der Geer and Schoof gave a definition of a function h 0 on metrized line bundles that resembles properties of the dimension l ( D ) of H 0 ( X , ℒ ( D ) ) , where D is a divisor on a curve X . In particular, they get a direct analogue of the Rieman-Roch theorem. For three theorems of curves, notably Clifford’s theorem, we will propose arithmetic analogues.