When Claude Chabauty was appointed to the University of Grenoble in 1954, Marcel Brelot, his predecessor in the Chair of Differential and Integral Calculus, had not long launched "The Annales of the Fourier Institute", which superseded the mathematical-physical series of "The Annales of the University of Grenoble".
From 1954 onwards, while he was in charge of the Laboratory of Pure Mathematics, Claude Chabauty helped the journal by procuring the infrastructure and resources that permit its regular publication.
It should be remarked that the Laboratory of Pure Mathematics of Grenoble, as it exists today, was in fact shaped by Claude Chabauty. He directed it for more than 22 years; he steered it through the pitfalls of a period of rapid growth; he played a decisive role in the recruitments in the sixties; he organised and "ran in" its various services. He also organised in great detail its installation in the building, constructed in 1966, which has become the new "Institute Fourier".
The academic environment of Grenoble has indeed been favourable to mathematicians; but it is thanks to the clear sightedness and good judgment of Claude Chabauty that they have been able to take advantage of these circumstances. The exceptional role that he has played in the orientation of the Laboratory is largely explained through his culture and the importance of his mathematical work. His teaching, richly innovative, has inspired a number of our best students, several of whom have gone on to enrich the community of French mathematics.
The fundamental mathematical work of Claude Chabuty has been devoted to the Diophantine problems, to approximations and to the geometry of numbers. He was one of the first mathematicians to use, with equal success, both classical analysis and the p-adic analysis to surmount the difficulties that arise in Diophantine problems.
His thesis, defended in 1938, contained spectacular results, in particular, the following theorem
Let K denote a field of numbers possessing at least two infinite non real places. Let N denote the norm function over K/Q, L a non-degenerate lattice of rank 3 and r a rational number, then the equation N(x) = r has only a finite number of solutions in L.This statement, whose proof relies particularly on the methods of p-adic analysis along the lines originated by T. Skolem, generalises the well-known theorem of Thue on the finite number of solutions of an equation of type f(x,y) = a where f is a form of greater than or equal to 3 and another theorem of T. Skolem for forms of 3 variables in a field of degree 5.