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Modularity of Higher Theta Series III: Proof of the Modularity Conjecture
Tony Feng, Zhiwei Yun, Wei Zhang
We prove the Modularity Conjecture for higher theta series on moduli stacks of Hermitian shtukas. For general linear shtukas, we establish a more refined phenomenon that we call su…
Arithmetic volumes of moduli stacks of Shtukas
Tony Feng, Zhiwei Yun, Wei Zhang
We define and study "tautological classes" in the cohomology of moduli stacks of shtukas, pursuing two directions of applications. First, we prove a formula relating the "arithmeti…
Higher Siegel--Weil formula for unitary groups II: corank one terms
Tony Feng, Benjamin Howard, Mikayel Mkrtchyan
We prove the higher Siegel--Weil formula for \emph{corank one} terms, relating (1) the central derivatives of corank one Fourier coefficients of Siegel--Eisenstein ser…
Modularity of higher theta series II: Chow group of the generic fiber
Tony Feng, Adeel A. Khan
Higher theta series on moduli spaces of Hermitian shtukas were constructed by Feng--Yun--Zhang and conjectured to be modular, parallel to classical conjectures in the Kudla program…