Atiyah–Bott fixed-point theorem: Difference between revisions

Revision as of 15:16, 12 September 2019

Revision as of 07:35, 14 November 2019

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In the recollection of [[William Fulton (mathematician)|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 {{harvtxt|Kondyrev|Prikhodko|2018}} by expressing both sides of the formula as appropriately chosen [[categorical trace]]s.

==See also==

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*{{Citation|first1=Michael F.|last1= Atiyah|author1-link=Michael Atiyah|first2= Raoul|last2= Bott |author2-link=Raoul Bott| title=A Lefschetz Fixed Point Formula for Elliptic Complexes: I |journal=[[Annals of Mathematics]] | series = Second Series|volume= 86|issue=2 |year= 1967|pages= 374–407|doi=10.2307/1970694|jstor=1970694}} and {{citation|first1=Michael F.|last1= Atiyah|author1-link=Michael Atiyah|first2= Raoul|last2= Bott |author2-link=Raoul Bott| |title=A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications

|journal=[[Annals of Mathematics]] | series = Second Series|volume=88|issue=3|year= 1968|pages=451–491|doi=10.2307/1970721|jstor=1970721}}. These gives the proofs and some applications of the results announced in the previous paper.

*{{Citation|title=Categorical Proof of Holomorphic Atiyah–Bott Formula|last1=Kondyrev|first1=Grigory|last2=Prikhodko|first2=Artem|journal=J. Inst. Math. Jussieu|year=2018|pages=1–25|doi=10.1017/S1474748018000543|arxiv=1607.06345}}

==External links==