was other input, as is suggested by the alternate name Woods Hole fixed-point theorem that was used in the past (referring properly to the case of isolated fixed points). A 1964 meeting at Woods Hole brought together a varied group: Eichler started the interaction between fixed-point theorems and automorphic forms. Shimura played an important part in this development by explaining this to Bott at the Woods Hole conference in 1964. As Atiyah puts it: [at the conference]...Bott and I learnt of a conjecture of Shimura concerning a generalization of the Lefschetz formula for holomorphic maps. After much effort we convinced ourselves that there should be a general formula of this type [...]; . and they were led to a version for elliptic complexes. In the recollection of William Fulton, who was also present at the conference, the first to produce a proof was Jean-Louis Verdier. Proofs In the context of algebraic geometry, the statement applies for smooth and proper varieties over an algebraically closed field. This variant of the Atiyah–Bott fixed point formula was proved by by expressing both sides of the formula as appropriately chosen categorical traces. See also Bott residue formula Notes References . This states a theorem calculating the Lefschetz number of an endomorphism of an elliptic complex. and . These gives the proofs and some applications of the results announced in the previous paper. External links Fixed-point theorems Theorems in differential topology