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Acta Mathematica Vietnamica

WEAKLY BOUNDED HEIGHT ON MODULAR CURVES

icon-email P. HABEGGER

Abstract

We study the intersection of a fixed plane algebraic curve C with modular curves of varying level. The height of points in such intersections cannot be bounded from above independently of the level when C is defined over the field of algebraic numbers. But we find a certain class of curves C for which the height is bounded logarithmically in the level. This bound is strong enough to imply certain finiteness result. Such evidence leads to a conjecture involving a logarithmic height bound unless C is of so-called special type. We also discuss connections to recent progress on conjectures concerning unlikely intersections.

8.1.30PHP Version371msRequest Duration4MBMemory UsageGET acta/{alias}/{type}/{alias_article}Route
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
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      Metadata
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