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Award ID contains: 1901642

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  1. ; ; (, Inventiones mathematicae)
    Abstract We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the$$r^{\mathrm{th}}$$ r th central derivative of non-singular Fourier coefficients of a normalized Siegel–Eisenstein series, and (2) the degree of special cycles of “virtual dimension 0” on the moduli stack of hermitian shtukas with$$r$$ r legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein series. 
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  2. ; ; ; ; (, Inventiones mathematicae)
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  3. (, Pure and Applied Mathematics Quarterly)
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  4. ; (, Essential Number Theory)
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  5. ; ; ; (, Annals of Mathematics)
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  6. ; ; (, Pure and Applied Mathematics Quarterly)
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  7. (, Annals of mathematics)
    null (Ed.)
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  8. ; ; (, Compositio Mathematica)
    null (Ed.)
    We define variants of PEL type of the Shimura varieties that appear in the context of the arithmetic Gan–Gross–Prasad (AGGP) conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral models of these Shimura varieties and formulate for them conjectures on arithmetic intersection numbers. We prove some of these conjectures in low dimension. 
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  9. (, Science China Mathematics)
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