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Riemann's Zeta Function

- Adam J. Harper, Tony Feng
- Mathematics
- 2014

Preface This document grew out of lecture notes for a course taught in Cambridge during Lent 2014 by Adam Harper on the theory of the Riemann zeta function. There are likely to be errors, which are… Expand

Privately Evaluating Decision Trees and Random Forests

- David J. Wu, Tony Feng, M. Naehrig, K. Lauter
- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 1 October 2016

TLDR

p-divisible groups

- Tony Feng, Alexander Bertoloni Meli
- Mathematics
- 2016

Let E be an elliptic curve over a eld k; imagine for the moment that k is of characteristic 0, although we will also be very interested in the characteristic p case. The p-divisible group of E is… Expand

EXTENSIONS OF VECTOR BUNDLES ON THE FARGUES-FONTAINE CURVE

- C. Birkbeck, Tony Feng,
+4 authors Lynnelle Ye - MathematicsJournal of the Institute of Mathematics of…
- 1 May 2017

Abstract 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 condition… Expand

The Spectral Hecke Algebra

- Tony Feng
- Mathematics
- 9 December 2019

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. This is a Hecke… Expand

Nearby cycles of parahoric shtukas, and a fundamental lemma for base change

- Tony Feng
- MathematicsSelecta Mathematica
- 7 November 2017

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 perverse sheaves on… Expand

Epipelagic Langlands parameters and L-packets for unitary groups

- Tony Feng, N. Ronchetti, Cheng-Chiang Tsai
- MathematicsInternational Journal of Number Theory
- 7 November 2017

Reeder and Yu have recently given a new construction of a class of supercuspidal representations called epipelagic representations [M. Reeder and J.-K. Yu, Epipelagic representations and invariant… Expand

Representation Theory in Intermediate Characteristic

We are going to work p-locally, i.e. fix a prime p and work over a “field” in which all other primes are invertible. In algebra, this means that we are working in a characteristic 0 field or a field… Expand

Néron models, Tamagawa factors, and Tate-Shafarevich groups

Obstruction to (1). If the answer to (1) is affirmative, with smooth proper R-model X, then the smooth and proper base change theorems for étale cohomology imply upon choosing a place of Fs over that… Expand

Étale Steenrod operations and the Artin–Tate pairing

- Tony Feng
- MathematicsCompositio Mathematica
- 1 June 2017

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 analog of the Cassels–Tate pairing. Tate asked if this pairing… Expand

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