Genus 2 curves and modular forms on Shimura curves
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srinivasan-vijayrs-phd-math-2026-thesis.pdf
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Author(s)
Srinivasan, Vijay Ravi
Advisor(s)
Zhang, Wei
Date Issued
May 2026
Publisher
Massachusetts Institute of Technology
Abstract
This thesis studies geometric aspects of modular forms on Shimura curves over the rational numbers. The motives associated to modular forms of weight 2 have been long understood as isogeny factors in the Jacobians of Shimura curves. For modular forms of weight at least 3, we provide a new incarnation of the motive associated to such a modular form, built from the universal genus 2 curve over a Shimura curve. To illustrate the utility of such a description, we construct generalized diagonal cycles relevant to the central vanishing properties of triple-product L-series (via the conjectures of Beilinson).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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