Theory of the Siegel Modular Variety
Jae-Hyun Yang
TL;DR
This paper explores the arithmetic and geometric aspects of the Siegel modular variety, including modular forms, Hecke theory, and motives, providing a comprehensive theoretical framework.
Contribution
It offers a detailed theoretical analysis of Siegel modular varieties, integrating modular forms, Hecke operators, and motives, advancing understanding in arithmetic geometry.
Findings
Development of the theory of Siegel modular forms
Insights into the geometric properties of the variety
Discussion of motives and cohomology related to Siegel modular forms
Abstract
In this paper, we discuss the theory of the Siegel modular variety in the aspects of arithmetic and geometry. This article covers the theory of Siegel modular forms, the Hecke theory, a lifting of elliptic cusp forms, geometric properties of the Siegel modular variety, (hypothetical) motives attached to Siegel modular forms and a cohomology of the Siegel modular variety.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Advanced Mathematical Identities