We prove an algebraic version of a classical theorem in topology, asserting that an abelian p-group action on a smooth projective variety of positive dimension cannot fix exactly one point. When the group has only two elements, we prove that the number of fixed points cannot be odd. The main tool is a construction originally used by Rost in the context of the degree formula. The framework of diagonalisable groups allows us to include the case of base fields of characteristic p.

Haution, O. (2020). Diagonalisable p-groups cannot fix exactly one point on projective varieties. JOURNAL OF ALGEBRAIC GEOMETRY, 29(2), 373-402 [10.1090/jag/749].

Diagonalisable p-groups cannot fix exactly one point on projective varieties

Haution O.
2020

Abstract

We prove an algebraic version of a classical theorem in topology, asserting that an abelian p-group action on a smooth projective variety of positive dimension cannot fix exactly one point. When the group has only two elements, we prove that the number of fixed points cannot be odd. The main tool is a construction originally used by Rost in the context of the degree formula. The framework of diagonalisable groups allows us to include the case of base fields of characteristic p.
Articolo in rivista - Articolo scientifico
actions of p-groups, fixed points, degree formula
English
2020
29
2
373
402
reserved
Haution, O. (2020). Diagonalisable p-groups cannot fix exactly one point on projective varieties. JOURNAL OF ALGEBRAIC GEOMETRY, 29(2), 373-402 [10.1090/jag/749].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/449259
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