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Riemann's Zeta Function
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
Privately Evaluating Decision Trees and Random Forests
Two protocols for privately evaluating decision trees and random forests are developed and an extension of the semi-honest protocol is given that is robust against malicious adversaries and demonstrates a tenfold improvement in computation and bandwidth.
p-divisible groups
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
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
The Spectral Hecke Algebra
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
Nearby cycles of parahoric shtukas, and a fundamental lemma for base change
  • Tony Feng
  • Mathematics
    Selecta 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
Epipelagic Langlands parameters and L-packets for unitary groups
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
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
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
Étale Steenrod operations and the Artin–Tate pairing
  • Tony Feng
  • Mathematics
    Compositio 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