1 citations · 1 across the 7 of their papers we have counts for
9 papers
Local Langlands functoriality for Yu's supercuspidals II: Fargues--Scholze's parametrization
Sean Cotner, Tony Feng
This is the second of two papers dedicated to the explicit computation of the Fargues--Scholze correspondence. We compute the Tate cohomology of cuspidal representations arising fr…
Local Langlands functoriality for Yu's supercuspidals I: Kaletha's parametrization
Sean Cotner, Tony Feng
This is the first of two papers dedicated to the explicit computation of the Fargues--Scholze correspondence. In this first part, we construct (inspired by, and extending, Kaletha'…
Steenrod operations and symplectic arithmetic duality
Tony Feng
This expository article elaborates upon my talk at the 2025 AMS Summer Institute on Algebraic Geometry. It gives an introduction to a conjecture from Tate's 1966 Séminaire Bourbaki…
Eigenweights for arithmetic Hirzebruch Proportionality
Tony Feng
Prior work of Feng--Yun--Zhang established a (Higher) Arithmetic Hirzebruch Proportionality Principle, expressing the arithmetic volumes of moduli stacks of shtukas in terms of dif…
Prismatic Steenrod operations and arithmetic duality on Brauer groups
Shachar Carmeli, Tony Feng
We construct and analyze the "syntomic Steenrod algebra", which acts on the mod syntomic cohomology (also known as etale-motivic cohomology) of algebraic varieties in character…
Derived structures in the Langlands Correspondence
Tony Feng, Michael Harris
We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived He…
Geometric Langlands duality for periods
Tony Feng, Jonathan Wang
We study conjectures of Ben-Zvi--Sakellaridis--Venkatesh that categorify the relationship between automorphic periods and -functions in the context of the Geometric Langlands eq…
Modular functoriality in the Local Langlands Correspondence
Tony Feng
We develop a theory of Smith--Treumann localization in the context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We then apply this theory to prove som…
Mirror symmetry and the Breuil-Mézard Conjecture
Tony Feng, Bao Le Hung
The Breuil-Mézard Conjecture predicts the existence of hypothetical "Breuil-Mezard cycles" in the moduli space of mod Galois representations of $\mathrm{Gal}(\overline{\mathbb{…