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Feng-Yun-Zhang have proved a function field analogue of the arithmetic Siegel-Weil formula, relating special cycles on moduli spaces of unitary shtukas to higher derivatives of Eisenstein series. We prove an extension of this formula in a low-dimensional case, and deduce from it a Gross-Zagier style formula expressing intersection multiplicities of cycles in terms of higher derivatives of base-change L-functions. 

On an orthogonal Shimura variety, one has a collection of arithmetic special cycles in the Gillet–Soulé arithmetic Chow group. We describe how these cycles behave under pullback to an embedded orthogonal Shimura variety of lower dimension. The bulk of the paper is devoted to cases in which the special cycles intersect the embedded Shimura variety improperly, which requires that we analyze logarithmic expansions of Green currents on the deformation to the normal bundle of the embedding. 

ABSTRACT Using the youngest detrital-zircon date(s) of a sedimentary deposit to constrain its maximum depositional age (MDA) is a widespread and growing application of geochronology. Most MDA studies analyze zircon grains at random, but this strategy can be costly and inefficient in cases where the youngest age group is only a small fraction of the population. We propose that handpicking sharply faceted zircon grains will increase the likelihood of encountering first-cycle zircon that have not undergone significant sedimentary transport, thus producing MDA estimates that are closer to the depositional age. We evaluate this procedure by conducting intra-sample comparisons of randomly selected versus handpicked zircon separates from 30 samples analyzed via laser-ablation–inductively coupled plasma–mass spectrometry (LA–ICP–MS). Our results show that handpicking zircon produces an overall shift towards younger ages in comparison to their randomly analyzed counterparts by an average of ∼ 406 Myr. In randomly analyzed separates, only 1.6% of grains were within 5 Myr of an independent estimate of the MDA, while handpicked separates contained 14.2%, an approximately nine-fold increase. However, handpicking can also lead to selection of older grains if they have been minimally transported, as with one handpicked Mesozoic sample that yielded 81% of ∼ 1.1 Ga zircon interpreted to be derived from a local granitic source. Handpicking is most effective in samples where young, sharply faceted grains are diluted by older, rounded grains, as with one sample that exhibited an ∼ 18-fold increase in the proportion of near-depositional-age zircons relative to its counterpart where grain selection was random. Because handpicking zircon imparts a severe bias on the resulting U–Pb age distribution, we recommend that two separate aliquots be used for quantitative provenance characterization through random analysis and MDA analysis through handpicking. 

Abstract We prove an invariance property of intersections of Kudla–Rapoport divisors on a unitary Rapoport–Zink space.