Shimura Varieties Seminar
Shimura Varieties Seminar
Participants: Kevin Dao and Ryan Tamura.Â
References: Introduction to Shimura Varieties by Milne, An Example-Based Introduction to Shimura Varieties by Kai-wen Lan.
Advisor: Tonghai Yang.
Participants: Kevin Dao and Ryan Tamura.Â
References: Introduction to Shimura Varieties by Milne, An Example-Based Introduction to Shimura Varieties by Kai-wen Lan.
Advisor: Tonghai Yang.
Readings from Milne's Introduction to Shimura Varieties.
Hermitian Symmetric Domains p. 5-21.
Hodge Structures and their Classifying Spaces p. 22-31.
Locally Symmetric Varieties p. 32-41.
Connected Shimura Varieties p. 43-51
Shimura Varieties p. 52-66.
The Siegel Modular Variety p. 67-75.
Shimura varieties of Hodge type p. 76-78. (Skipped)
PEL Shimura varieties p. 79-89. (End Goal)
Statements of Main Theorems in later chapters.
Things not included in this list that should be included at some point: relationship with the (arithmetic) Langlands program, the work of Jacob Tsimerman, Ananth Shankar, and other modern developments for Shimura Varieties, local theta correspondence, theta correspondence, Gross-Zagier formula, Gross-Zagier formula in higher dimensions, Siegel-Weil formula, generlizations of the Siegel-Weil formula, Kudla's "Algebraic Cycles on Shimura Varieties of Orthogonal Type", Chao Li's "From sum of two squares to arithmetic Siegel-Weil formulas", and more.