17 citations · 86 across the 20 of their papers we have counts for
22 papers
Archimedean arithmetic Siegel--Weil formula for general weights over Shimura curves
Yifeng Liu
We prove an averaging formula for the canonical archimedean height pairing of special divisors with weights over orthogonal and unitary Shimura curves in terms of derivatives of Wh…
Bessel periods and Selmer groups over ordinary Rankin--Selberg eigenvariety
Yifeng Liu
We introduce the notion of ordinary distributions for unitary groups and their Rankin--Selberg products, based on which we (re)define the ordinary eigenvarieties. In both definite…
Anticyclotomic -adic -functions for Rankin--Selberg product
Yifeng Liu
We construct -adic -functions for Rankin--Selberg products of automorphic forms of hermitian type in the anticyclotomic direction for both root numbers. When the root number…
A -adic arithmetic inner product formula
Daniel Disegni, Yifeng Liu
Fix a prime number and let be a CM extension of number fields in which splits relatively. Let be an automorphic representation of a quasi-split unitary group of e…
Theta correspondence for almost unramified representations of unitary groups
Yifeng Liu
In this note, we introduce the notion of almost unramified representations of quasi-split unitary groups of even ranks with respect to an unramified quadratic extension of local fi…
Fourier-Jacobi cycles and arithmetic relative trace formula (with an appendix by Chao Li and Yihang Zhu)
Yifeng Liu
In this article, we develop an arithmetic analogue of Fourier--Jacobi period integrals for a pair of unitary groups of equal rank. We construct the so-called Fourier--Jacobi cycles…
Chow groups and -derivatives of automorphic motives for unitary groups, II
Chao Li, Yifeng Liu
In this article, we improve our main results from \emph{Chow groups and -derivatives of automorphic motives for unitary groups} in two direction: First, we allow ramified places…
Chow groups and -derivatives of automorphic motives for unitary groups
Chao Li, Yifeng Liu
In this article, we study the Chow group of the motive associated to a tempered global -packet of unitary groups of even rank with respect to a CM extension, whose global ro…
On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives
Yifeng Liu, Yichao Tian, Liang Xiao +2
In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the…
Isolation of cuspidal spectrum, with application to the Gan--Gross--Prasad conjecture
Raphaël Beuzart-Plessis, Yifeng Liu, Wei Zhang +1
We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof…
Supersingular locus of Hilbert modular varieties, arithmetic level raising and Selmer groups
Yifeng Liu, Yichao Tian
This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus of modular curves to all Shimura varieties given b…
Monodromy map for tropical Dolbeault cohomology
Yifeng Liu
We define monodromy maps for tropical Dolbeault cohomology of algebraic varieties over non-Archimedean fields. We propose a conjecture of Hodge isomorphisms via monodromy maps, and…
Weight decomposition of de Rham cohomology sheaves and tropical cycle classes for non-Archimedean spaces
Yifeng Liu
We construct a functorial decomposition of de Rham cohomology sheaves, called weight decomposition, for smooth analytic spaces over non-Archimedean fields embeddable into $\mathbf{…
Hirzebruch-Zagier cycles and twisted triple product Selmer groups
Yifeng Liu
Let be an elliptic curve over and be another elliptic curve over a real quadratic number field. We construct a -motive of rank , together with a…
On -adic Waldspurger formula
Yifeng Liu, Shouwu Zhang, Wei Zhang
In this article, we study -adic torus periods for certain -adic valued functions on Shimura curves coming from classical origin. We prove a -adic Waldspurger formula for t…
Bounding cubic-triple product Selmer groups of elliptic curves
Yifeng Liu
Let be a modular elliptic curve over a totally real cubic field. We have a cubic-triple product motive over constructed from through multiplicative induction;…
Enhanced adic formalism and perverse t-structures for higher Artin stacks
Yifeng Liu, Weizhe Zheng
In this sequel of arXiv:1211.5294 and arXiv:1211.5948, we develop an adic formalism for étale cohomology of Artin stacks and prove several desired properties including the base cha…
Gluing restricted nerves of -categories
Yifeng Liu, Weizhe Zheng
In this article, we develop a general technique for gluing subcategories of -categories. We obtain categorical equivalences between simplicial sets associated to certain mu…
Uniqueness of Fourier-Jacobi models: the Archimedean case
Yifeng Liu, Binyong Sun
We prove uniqueness of Fourier-Jacobi models for general linear groups, unitary groups, symplectic groups and metaplectic groups, over an archimedean local field.
On quadratic distinction of automorphic sheaves
Yifeng Liu
We prove a geometric version of a classical result on the characterization of an irreducible cuspidal automorphic representation of being the base cha…
Relative trace formulae toward Bessel and Fourier-Jacobi periods of unitary groups
Yifeng Liu
We propose a relative trace formula approach and state the corresponding fundamental lemma toward the global restriction problem involving Bessel or Fourier-Jacobi periods of unita…
A non-archimedean analogue of Calabi-Yau theorem for totally degenerate abelian varieties
Yifeng Liu
We show an example of a non-archimedean version of the Calabi-Yau theorem in complex geometry. Precisely, we consider totally degenerate abelian varieties and certain probability m…