Co-rank 1 11 Arithmetic Siegel–Weil IV: Analytic local-to-global

Abstract This is the fourth in a sequence of four papers, where we prove the arithmetic Siegel–Weil formula in co-rank 1 1 1 for Kudla–Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even arithmetic dimension. Our arithmetic Siegel–Weil formula implies that degrees of Kudla–Rapoport arithmetic special 1 1 1 -cycles are encoded in near-central first derivatives of unitary Eisenstein series Fourier coefficients. In this paper, we pin down precise normalizations for some U (m, m) U (m, m) upper U left parenthesis m comma m right parenthesis Siegel Eisenstein series, give local Siegel–Weil special value formulas with explicit constants, and record a geometric Siegel–Weil result for degrees of complex 0 0 0 -cycles. Using these, we complete the proof of our arithmetic Siegel–Weil results by patching together the local main theorems from our companion papers.