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You are here: FRIAS Fellows Fellows 2019/20 Dr. Oliver Bräunling

Dr. Oliver Bräunling

University of Freiburg
Junior Fellow
October 2017 - July 2018


  • Grundstudium Georg-August-Universität Göttingen
  • Promotion an der University of Nottingham (United Kingdom)

Selected Publications

FRIAS Research Project

Algebraic K-theory and the mystery of special algebraic structures in characteristic p>

Algebraic K-theory is a theory encoding deep arithmetic information. At the advent of this theory in the 1950s it was not even expected that it would possess this remarkable feature, and there has been a success story over the following decades, ever again surprising with new connections to other fields of pure mathematics. A poorly understood aspect is that in positive characteristic p > 0, the structure of the etale fundamental group (at the same prime p) is known to be extremely complicated and mysterious. Correspondingly, one should expect that the structure of p-torsion etale constructible sheaves is very rich. One may investigate the latter using positive characteristic versions of the Riemann-Hilbert correspondence and categories of crystals. I want to understand how this arithmetic complexity interacts with the K-theory of these categories.