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A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.

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algebraic proof of Atiyah-Bott fixed point formula?

I am not sure this is the best place to learn the subject, but at least this book is an algebraic reference: Riemann-Roch algebra By William Fulton, Serge Lang more precisely VI \S 9 Lefschetz-Riema …
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6 votes
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Equivariant Riemann-Hurwitz

This is a well known and well understood problem when the base field is $\mathbb C$. It was first studied by Chevalley and Weil (almost a century ago !) who were interested in modular curves (what els …
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