Counting Drinfeld modules with prescribed local conditions

DOI10.1007/s40993-023-00500-7arXiv2209.05576OpenAlexW4391776952MaRDI QIDQ6196075

Tristan Phillips

Publication date: 14 March 2024

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.05576

zbMATH Keywords

Drinfeld modulesglobal function fieldsBatyrev-Manin conjecturegeometry of numbersweighted projective stacks

Mathematics Subject Classification ID

Rational points (14G05) Counting solutions of Diophantine equations (11D45) Arithmetic aspects of modular and Shimura varieties (11G18) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Heights (11G50)

Cites Work

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• Semi-simplicity of the Galois representations attached to Drinfeld modules over fields of ``infinite characteristics
• Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
• Squarefree values of polynomial discriminants. I
• Heights and isogenies of Drinfeld modules
• Heights on stacks and a generalized Batyrev–Manin–Malle conjecture
• Local and global densities for Weierstrass models of elliptic curves
• On the distribution of analytic ranks of elliptic curves

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