The Royal Swedish Academy of Sciences awards 423 000 USD (2,5 million SEK) to research in mathematics from the Anna-Greta and Holger Crafoord Fund. 1,6 million SEK is shared between two mathematics, working within algebraic geometry, and 900 000 SEK is awarded to Swedish research within the same field.

The Royal Swedish Academy of Sciences had decided to award the 1988 Crafoord Prize (1,6 million SEK) jointly to **Professor Pierre Deligne**, Institute for Advanced Study, Princeton, New Jersey, USA and **Professor Alexander Grothendieck**, Université des Sciences et Techniques du Languedoc, Montpellier, France, for their fundamental research in algebraic geometry, especially the introduction of étale cohomolgy (Grothendieck) and its application to various fields of mathematics (Grothendieck and Deligne), including the proof of the Weil conjectures.

Swedish research within algebraic geometry will at the same time receive 900 000 SEK as grants from the Anna-Greta and Holger Crafoord Fund.

The Prize will be awarded at a solemn ceremony at the Royal Swedish Academy on Wednesday September 21, 1988.

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The Prizewinners are honored for their research in pure mathematics, however related results have e.g. been used in connection with the construction of error-correcting codes which are used e.g. in communication with satellites.

Algebraic geometry is one of the oldest part of mathematics and in its most primitive form it is about the structure of solutions to polynomial equations in several variables. There is both a continuous aspect of this problem (one studies e.g. solutions among the complex numbers) and also a discrete aspect (one studies e.g. solutions among the integers) and for hundreds of years mathematicians have dreamed of unifying these two approaches, so as to get e.g. general methods of proof in number theory. But it is only during the last 25 years that this dream has been realized (although lots of things remain to be done). In connection with this an important driving force has been some conjectures (the “Weil conjectures”) that were put forward in 1948 by the French-American mathematician André Weil (born 1906), in particular e.g. about the number of solutions of polynomial equations modulo a prime p, when p becomes big. These conjectures were completely proved by Alexandre Grothendieck and Pierre Deligne about 15 years ago. In connection with this notion of étale co homology has played an important role and during their study of this notion and its applications. Grothendieck and Deligne revolutionized algebraic geometry. Later developments in algebraic geometry (Faltings’ work about e.g. the big theorem of Fermat, Mori’s work about models of algebraic varieties and work by the prize winners and others) have demonstrated in a very convincing way the enormous potential and force of the ideas of the prizewinners.

**Pierre Deligne** was born October 3, 1944 in Brussels, Belgium. He studied in Paris and in 1973 he became Professor in Mathematics at the Institute des Hautes Etudes Scientifiques in Paris. Since 1985 he is professor in Mathematics at the Institute for Advanced Study in Princeton, New Jersey, USA.

**Alexander Grothendieck** was born on March 28, 1928 in Berlin. He spent a large part of his youth in France and he was professor at the institute des Hautes Etudes Scientifiques in Paris 1959-1971. After two years at the Collége de France he is (since 1973) now professor in mathematics at the Université des Sciences et Techniques du Languedoc, Montpellier, France. He is also a professor at the Centre National de la Recherche Scientifique (CNRS).