Cohomological interpretation of quadratic modular symbols
Pilar Bayer, Iv\'an Blanco-Chac\'on, Alberto F. Boix
TL;DR
This paper provides a cohomological framework for quadratic modular symbols on Shimura curves and includes explicit homology computations, enhancing understanding of their algebraic and geometric properties.
Contribution
It introduces a cohomological interpretation of quadratic modular symbols on Shimura curves, expanding the theoretical foundation and computational methods.
Findings
Cohomological interpretation of quadratic modular symbols established
Explicit homology computations for certain Shimura curves performed
Enhanced understanding of algebraic and geometric properties of modular symbols
Abstract
Bayer and Blanco-Chac\'on have recently defined quadratic modular symbols for the Shimura curves X(D,N) attached to Eichler orders of level N of an indefinite quaternion rational algebra of discriminant D. In this paper, we give a cohomological interpretation of these quadratic modular symbols. Explicit computations for the homology of some Shimura curves are also provided.
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Taxonomy
TopicsAdvanced Mathematical Identities · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory