The following was written by Gerard van der Geer, President of the Foundation Compositio Mathematica. Additional history of the Prize as well as a list of past winners can be found here.

Every three years, the Foundation Compositio Mathematica awards a prize for the best paper published in Compositio Mathematica in a three-year period. The Compositio Prize 2021 for the period 2017–2019 has been awarded to the two papers:

Daniel Huybrechts,
The K3 category of a cubic fourfold,
Compositio Math. 153 (2017), 58–620. https://doi.org/10.1112/S0010437X16008137

Colin J. Bushnell† and Guy Henniart,
Local Langlands correspondence and ramification for Carayol representations,
Compositio Math. 155 (2019), 195–2038. https://doi.org/10.1112/S0010437X19007449

The article The K3 category of a cubic fourfold by Daniel Huybrechts establishes a collection of important results about Kuznetsov components of smooth cubic fourfolds. The Kuznetsov component is a subcategory of the derived category. Huybrechts proves that for a smooth cubic fourfold X, there are only finitely many isomorphism classes of fourfolds whose Kuznetsov component is Fourie–Mukai equivalent to that of X, and only one such class when X is very general. It also gives a criterion for the Kuznetsov component to be equivalent to the derived category of a twisted K3 surface. This influential article should pave the way to solving the mysterious rationality problem for cubic fourfolds.

The article Local Langlands correspondence and ramification for Carayol representations by Colin Bushnell and Guy Henniart constitutes major progress in the study of local Langlands. The authors establish a complete classification of Herbrand functions arising from totally wild simple characters of Carayol type. They use this to completely describe the ramification behaviour of the corresponding Weil group representations.

Gerard van der Geer
President
Foundation Compositio Mathematica

†Colin Bushnell sadly passed away on 1 January 2021