Genus of abstract modular curves with level-ℓ structures
-
Anna Cadoret
and
Akio Tamagawa
Abstract
We prove – in arbitrary characteristic – that the genus of abstract modular curves associated to bounded families of continuous geometrically perfect
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: ANR-10-JCJC 0107
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1155
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 22340006
Award Identifier / Grant number: 15H03609
Funding statement: This work was partly supported by RIMS, Kyoto University. The first author was also partly supported by the project ANR-10-JCJC 0107 from the Agence Nationale de la Recherche and the NSF grant DMS-1155. Most of this work was elaborated during stays of the first author at RIMS and IAS. She would like to thank both institutes for their hospitality. The second author was partly supported by JSPS KAKENHI Grant Numbers 22340006, 15H03609.
Acknowledgements
The first author would like to thank Michael Larsen for his interest and stimulating discussions on the topics of this paper while she visited him at Indiana University. The authors are grateful to the referee for numerous constructive comments.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Weak approximation for isotrivial families
- Genus of abstract modular curves with level-ℓ structures
- Strong shift equivalence and algebraic K-theory
- The solvable length of groups of local diffeomorphisms
- Positivity properties of metrics and delta-forms
- Iwasawa theory for the symmetric square of a modular form
- Cohomology and torsion cycles over the maximal cyclotomic extension
- Integrability of continuous bundles
- Kodaira dimension of moduli of special cubic fourfolds
Articles in the same Issue
- Frontmatter
- Weak approximation for isotrivial families
- Genus of abstract modular curves with level-ℓ structures
- Strong shift equivalence and algebraic K-theory
- The solvable length of groups of local diffeomorphisms
- Positivity properties of metrics and delta-forms
- Iwasawa theory for the symmetric square of a modular form
- Cohomology and torsion cycles over the maximal cyclotomic extension
- Integrability of continuous bundles
- Kodaira dimension of moduli of special cubic fourfolds
