Effective counting of the points of definable sets over finite fields

1994 ◽  
Vol 85 (1-3) ◽  
pp. 103-133 ◽  
Author(s):  
Michael D. Fried ◽  
Dan Haran ◽  
Moshe Jarden
Keyword(s):  
Finite Fields ◽  
Definable Sets

scholarly journals Pseudofinite difference fields

2019 ◽  
Vol 19 (02) ◽  
pp. 1950011
Author(s):  
Tingxiang Zou
Keyword(s):  
Finite Fields ◽  
Transcendence Degree ◽  
Order Property ◽  
Frobenius Automorphism ◽  
Difference Fields ◽  
Definable Sets ◽  
Partial Connection

We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we establish a partial connection between coarse dimension and transformal transcendence degree in these difference fields.

scholarly journals Pseudofinite difference fields and counting dimensions

2020 ◽  
Vol 21 (01) ◽  
pp. 2050022
Author(s):  
Tingxiang Zou
Keyword(s):  
Finite Fields ◽  
Transcendence Degree ◽  
Order Property ◽  
Frobenius Automorphism ◽  
Difference Fields ◽  
Definable Sets

We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we also discuss the possible connection between coarse dimension and transformal transcendence degree in these difference fields.

scholarly journals Motives for perfect PAC fields with pro-cyclic Galois group

2008 ◽  
Vol 73 (3) ◽  
pp. 1036-1050
Author(s):  
Immanuel Halupczok
Keyword(s):  
Galois Group ◽  
Finite Fields ◽  
Grothendieck Ring ◽  
Additional Information ◽  
Chow Motives ◽  
Closed Fields ◽  
Cohomological Invariant ◽  
Definable Sets ◽  
Grothendieck Rings ◽  
Algebraically Closed Fields

AbstractDenef and Loeser denned a map from the Grothendieck ring of sets definable in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling to apply any cohomological invariant to these sets. We generalize this to perfect, pseudo algebraically closed fields with pro-cyclic Galois group.In addition, we define some maps between different Grothendieck rings of definable sets which provide additional information, not contained in the associated motive. In particular we infer that the map of Denef-Loeser is not injective.

Asymptotic classes of finite structures

2007 ◽  
Vol 72 (2) ◽  
pp. 418-438 ◽  
Author(s):  
Richard Elwes
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Good Control ◽  
First Order ◽  
Finite Structures ◽  
Definable Sets

In this paper we consider classes of finite structures where we have good control over the sizes of the definable sets. The motivating example is the class of finite fields: it was shown in [1] that for any formula in the language of rings, there are finitely many pairs (d, μ) ∈ ω × Q>0 so that in any finite field F and for any ā ∈ Fm the size |ø(Fn,ā)| is “approximately” μ|F|d. Essentially this is a generalisation of the classical Lang-Weil estimates from the category of varieties to that of the first-order-definable sets.

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields

Maximum Distance Separable Hankel Rhotrices over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Maximum Distance ◽  
Maximum Distance Separable
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