arXiv subjects

Xiangqian Yang

Publications and source records attributed to Xiangqian Yang.

4 recordsLinked to original sources

arXiv2025

On the generic part of the cohomology of Shimura varieties of abelian type

This article contributes to the study of the generic part of the cohomology of Shimura varieties. Under a mild restriction of the characteristic of the coefficient field, we prove a torsion vanishing result for Shimura varieties of abelian type, confirming a conjecture by Hamann--Lee. Our proofs utilize the unipotent categorical local Langlands correspondence and, in contrast to previous works, do not rely on the endoscopic classification of representations or on other results established through trace formula techniques.

math.NT↗

arXiv2025

On Ihara's lemma for definite unitary groups

Clozel, Harris, and Taylor proposed a conjectural generalized Ihara's lemma for definite unitary groups. In this paper, we prove their conjecture with banal coefficients under some conditions. As an application, we prove a level-raising result for automorphic forms associated to definite unitary groups.

math.NT↗

arXiv2022

Information Design in Allocation with Costly Verification

A principal who values an object allocates it to one or more agents. Agents learn private information (signals) from an information designer about the allocation payoff to the principal. Monetary transfer is not available but the principal can costly verify agents' private signals. The information designer can influence the agents' signal distributions, based upon which the principal maximizes the allocation surplus. An agent's utility is simply the probability of obtaining the good. With a single agent, we characterize (i) the agent-optimal information, (ii) the principal-worst information, and (iii) the principal-optimal information. Even though the objectives of the principal and the agent are not directly comparable, we find that any agent-optimal information is principal-worst. Moreover, there exists a robust mechanism that achieves the principal's payoff under (ii), which is therefore an optimal robust mechanism. Many of our results extend to the multiple-agent case; if not, we provide counterexamples.

econ.TH↗

arXiv2022

Information Design in Optimal Auctions

We study the information design problem in a single-unit auction setting. The information designer controls independent private signals according to which the buyers infer their binary private values. Assuming that the seller adopts the optimal auction due to Myerson (1981) in response, we characterize both the buyer-optimal information structure, which maximizes the buyers' surplus, and the sellerworst information structure, which minimizes the seller's revenue. We translate both information design problems into finite-dimensional, constrained optimization problems in which one can explicitly solve for the optimal information structures. In contrast to the case with one buyer (Roesler and Szentes, 2017), we show that with two or more buyers, the symmetric buyer-optimal information structure is different from the symmetric seller-worst information structure. The good is always sold under the seller-worst information structure but not under the buyer-optimal information structure. Nevertheless, as the number of buyers goes to infinity, both symmetric information structures converge to no disclosure. We also show that in an ex ante symmetric setting, an asymmetric information structure is never seller-worst but can generate a strictly higher surplus for the buyers than the symmetric buyer-optimal information structure.

econ.TH↗