8 citations · 18 across the 14 of their papers we have counts for
16 papers
Modularity of higher theta series I: cohomology of the generic fiber
Tony Feng, Zhiwei Yun, Wei Zhang
In a previous paper we constructed higher theta series for unitary groups over function fields, and conjectured their modularity properties. Here we prove the generic modularity of…
Derived class field theory
Tony Feng, Michael Harris, Barry Mazur
We sketch the construction of a derived enhancement of the reciprocity isomorphism of class field theory. Details will appear in a forthcoming joint paper of the authors with A. Ra…
-spectra of cyclic defect
Tony Feng, David Treumann, Allen Yuan
Broué's Abelian Defect Conjecture predicts interesting derived equivalences between derived categories of modular representations of finite groups. We investigate a generalization…
Cyclic base change of cuspidal automorphic representations over function fields
Gebhard Böckle, Tony Feng, Michael Harris +2
Let be a split semi-simple group over a global function field . Given a cuspidal automorphic representation of satisfying a technical hypothesis, we prove that for a…
Higher theta series for unitary groups over function fields
Tony Feng, Zhiwei Yun, Wei Zhang
In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-sing…
Higher Siegel--Weil formula for unitary groups: the non-singular terms
Tony Feng, Zhiwei Yun, Wei Zhang
We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th central derivative of non-singular Fourier coefficients of a normalize…
Smith theory and cyclic base change functoriality
Tony Feng
Lafforgue and Genestier-Lafforgue have constructed the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields. We establish…
The Galois action on symplectic -theory
Tony Feng, Soren Galatius, Akshay Venkatesh
We study a symplectic variant of algebraic -theory of the integers, which comes equipped with a canonical action of the absolute Galois group of . We compute this ac…
The geometric distribution of Selmer groups of elliptic curves over function fields
Tony Feng, Aaron Landesman, Eric M. Rains
Fix a positive integer and a finite field . We study the joint distribution of the rank of , the -Selmer group of , and the -torsion in the Tate-Shafar…
The Spectral Hecke Algebra
Tony Feng
We introduce a derived enhancement of local Galois deformation rings that we call the "spectral Hecke algebra", in analogy to a construction in the Geometric Langlands program. Thi…
Epipelagic Langlands parameters and L-packets for unitary groups
Tony Feng, Niccolo Ronchetti, Cheng-Chiang Tsai
Reeder and Yu have recently given a new construction of a class of supercuspidal representations called epipelagic representations. We explicitly calculate the Local Langlands Corr…
Nearby cycles of parahoric shtukas, and a fundamental lemma for base change
Tony Feng
Using the Langlands-Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perv…
An Alternating Property for Higher Brauer Groups
Tony Feng
Using the calculus of Steenrod operations in étale cohomology developed in [Feng17], we prove that the analogue of Tate's pairing on higher Brauer groups is alternating on 2-torsio…
Etale Steenrod operations and the Artin-Tate pairing
Tony Feng
We prove a 1966 conjecture of Tate concerning the Artin-Tate pairing on the Brauer group of a surface over a finite field, which is the analogue of the Cassels-Tate pairing. Tate a…
Extensions of Vector Bundles on the Fargues-Fontaine Curve
Christopher Birkbeck, Tony Feng, David Hansen +4
We completely classify the possible extensions between semistable vector bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple…
Elliptic Curves with Full 2-Torsion and Maximal Adelic Galois Representations
David Corwin, Tony Feng, Zane Kun Li +1
In 1972, Serre showed that the adelic Galois representation associated to a non-CM elliptic curve over a number field has open image in GL_2(\hat{Z}). In Greicius' thesis, he devel…