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Higher Siegel--Weil formula for unitary groups: the non-singular terms
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We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the 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 unitary shtukas with 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.
Forward citations
Cited by 2 Pith papers
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Diagonal cycles on Shtukas and the adjoint $L$-function
For split almost simple groups over function fields, self-intersections of diagonal cycles on shtuka moduli, with determinant line-bundle insertions, equal higher derivatives of adjoint L-functions.
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Intersections of Hecke correspondences on the modular varieties of $\mathcal{D}$-elliptic sheaves
For prime rank r, the intersection number of a Hecke correspondence with the diagonal on the modular variety of D-elliptic sheaves equals r/(q-1) times sums of modified Hurwitz class numbers of imaginary orders.
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