KELLY, Shane

Title
Associate Professor
Field
algebraic geometry
Research interests
motivic homotopy theory, algebraic K-theory and applications to representation theory, class field theory, and birational geometry.
Current research

Recently, I have been generalising the topological methods in algebraic geometry developed by Voevodsky and others. Specifically, I am adapting these methods into frameworks (such as modulus pairs and derived schemes) which are sensitive to nilpotents, unipotent groups, and wild ramification.
Selected publications
  1. K-theory of valuation rings (joint with Matthew Morrow)
    (2021) Compositio Mathematica, 157, Issue 6, pp.1121-1142.
  2. Mixed Motives and Geometric Representation Theory in Equal Characteristic (joint with Jens Niklas Eberhardt)
    (2019) Selecta Mathematica, 25:30.
  3. Voevodsky motives and ldh descent
    (2017) Astérisque, 391, pp.125.
  4. Points in algebraic geometry (joint with Ofer Gabber)
    (2015) J. Pure Appl. Algebr., Volume 219, Issue 10, pp.4667-4680.
  5. Vanishing of Negative K-theory in positive characteristic
    (2014) Compositio Mathematica, 150, Issue 8, pp.1425-1434.

Memberships, Awards and

activities