A fixed point formula for varieties over finite fields.

Derangements in cosets of primitive permutation groups

Journal of Group Theory ◽

10.1515/jgth-2014-0030 ◽

2015 ◽

Vol 18 (1) ◽

Author(s):

Andrei Pavelescu

Keyword(s):

Fixed Point ◽

Finite Fields ◽

Permutation Groups ◽

Normal Subgroups ◽

Primitive Groups ◽

Branched Coverings ◽

Affine Groups ◽

Nonabelian Subgroup ◽

Projective Curves ◽

Curves Over Finite Fields

AbstractMotivated by questions arising in connection with branched coverings of connected smooth projective curves over finite fields, we study the proportion of fixed-point free elements (derangements) in cosets of normal subgroups of primitive permutations groups. Using the Aschbacher–O'Nan–Scott Theorem for primitive groups to partition the problem, we provide complete answers for affine groups and groups which contain a regular normal nonabelian subgroup.

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On Additive invariants of actions of additive and multiplicative groups

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is013003003jkt219 ◽

2013 ◽

Vol 12 (3) ◽

pp. 551-568 ◽

Cited By ~ 1

Author(s):

Wenchuan Hu

Keyword(s):

Fixed Point ◽

Algebraic Group ◽

Finite Fields ◽

Algebraic Variety ◽

Characteristic Zero ◽

Multiplicative Group ◽

Fixed Point Set ◽

Projective Varieties ◽

Point Set ◽

Multiplicative Groups

AbstractLet X be an algebraic variety with an action of either the additive or multiplicative group. We calculate the additive invariants of X in terms of the additive invariants of the fixed point set, using a formula of Białynicki-Birula. The method is also generalized to calculate certain additive invariants for Chow varieties. As applications, we obtain results on the Hodge polynomial of Chow varieties in characteristic zero and the number of points for Chow varieties over finite fields. As applications, we obtain the l-adic Euler-Poincaré characteristic for the Chow varieties of certain projective varieties over a field of arbitrary characteristic. Moreover, we show that the virtual Hodge (p,0) and (0,q)-numbers of the Chow varieties and affine algebraic group varieties are zero for all p,q positive.

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Bruhat Order on Partial Fixed Point Free Involutions

The Electronic Journal of Combinatorics ◽

10.37236/4396 ◽

2014 ◽

Vol 21 (4) ◽

Cited By ~ 2

Author(s):

Mahir Bilen Can ◽

Yonah Cherniavsky ◽

Tim Twelbeck

Keyword(s):

Fixed Point ◽

Zeta Function ◽

Finite Fields ◽

Generating Function ◽

Bruhat Order ◽

Symmetric Matrices ◽

Order Complex ◽

Orbit Closures

The order complex of inclusion poset $PF_n$ of Borel orbit closures in skew-symmetric matrices is investigated. It is shown that $PF_n$ is an EL-shellable poset, and furthermore, its order complex triangulates a ball. The rank-generating function of $PF_n$ is computed and the resulting polynomial is contrasted with the Hasse-Weil zeta function of the variety of skew-symmetric matrices over finite fields.

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