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- W1639846469 abstract "We study ``forms of the Fermat equation'' over an arbitrary field $k$, i.e. homogenous equations of degree $m$ in $n$ unknowns that can be transformed into the Fermat equation $X_1^m+...+X_n^m$ by a suitable linear change of variables over an algebraic closure of $k$. Using the method of Galois descent, we classify all such forms. In the case that $k$ is a finite field of characteristic greater than $m$ that contains the $m$-th roots of unity, we compute the Galois representation on $l$-adic cohomology (and so in particular the zeta function) of the hypersurface associated to an arbitrary form of the Fermat equation." @default.
- W1639846469 created "2016-06-24" @default.
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- W1639846469 date "2004-10-01" @default.
- W1639846469 modified "2023-09-27" @default.
- W1639846469 title "The zeta function of forms of Fermat equations" @default.
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- W1639846469 doi "https://doi.org/10.1142/9789812561800_0012" @default.
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