The Weil conjectures (Q2831703)

The author, a prominent Dutch number theorist (born 1935), discusses the history of an analogue of the Riemann conjecture, the so-called ``characteristic \(p\) formulation'', symbolized by pRH, which concerns solving equations over finite fields and has been studied from \textit{E. Artin}'s thesis [Math. Z. 19, 153--206, 207--246 (1924; JFM 50.0107.01)]. In the very technical paper, which is interrupted by exclamations of personal excitement and historical reflection, the author discusses the history of pRH from the work of H. Hasse and F. K. Schmidt through the partial proof and conjectures by A. Weil, the increasing connection to cohomology, the contributions by A. Grothendieck to the big strides into pRH by Pierre Deligne (born 1944). The paper concludes with a biography of Deligne and an extensive list of references.