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Relations between jacobians of modular curves of level p 2

Imin Chen, Bart De Smit, Martin Grabitz (2004)

Journal de Théorie des Nombres de Bordeaux

We derive a relation between induced representations on the group GL 2 ( / p 2 ) which implies a relation between the jacobians of certain modular curves of level p 2 . The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of GL 2 ( / p 2 ) .

Relative ampleness in rigid geometry

Brian Conrad (2006)

Annales de l’institut Fourier

We develop a rigid-analytic theory of relative ampleness for line bundles and record some applications to faithfully flat descent for morphisms and proper geometric objects. The basic definition is fibral, but pointwise arguments from the algebraic and complex-analytic cases do not apply, so we use cohomological properties of formal schemes over completions of local rings on rigid spaces. An analytic notion of quasi-coherence is introduced so that we can recover a proper object from sections of...

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