Newton polygons and congruence decompositions of 𝐿-functions over finite fields

1992 ◽  
pp. 221-241 ◽  
Author(s):  
Da Qing Wan
Keyword(s):  
Finite Fields ◽  
Newton Polygons

scholarly journals Symmetry and parity in Frobenius action on cohomology

2011 ◽  
Vol 148 (1) ◽  
pp. 295-303 ◽  
Author(s):  
Junecue Suh
Keyword(s):  
Finite Fields ◽  
Characteristic Zero ◽  
Betti Numbers ◽  
Newton Polygons ◽  
Smooth Variety ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Crystalline Cohomology ◽  
Lefschetz Theorem ◽  
Hard Lefschetz Theorem

AbstractWe prove that the Newton polygons of Frobenius on the crystalline cohomology of proper smooth varieties satisfy a symmetry that results, in the case of projective smooth varieties, from Poincaré duality and the hard Lefschetz theorem. As a corollary, we deduce that the Betti numbers in odd degrees of any proper smooth variety over a field are even (a consequence of Hodge symmetry in characteristic zero), answering an old question of Serre. Then we give a generalization and a refinement for arbitrary varieties over finite fields, in response to later questions of Serre and of Katz.

CONSTANCY OF NEWTON POLYGONS OF -ISOCRYSTALS ON ABELIAN VARIETIES AND ISOTRIVIALITY OF FAMILIES OF CURVES

2019 ◽  
pp. 1-39
Author(s):  
Nobuo Tsuzuki
Keyword(s):  
Finite Fields ◽  
Abelian Varieties ◽  
Newton Polygons ◽  
Families Of Curves

We prove constancy of Newton polygons of all convergent$F$-isocrystals on Abelian varieties over finite fields. Applying the constancy, we prove the isotriviality of proper smooth families of curves over Abelian varieties. More generally, we prove the isotriviality over projective smooth varieties on which any convergent$F$-isocrystal has constant Newton polygons.

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

Notes on three-pass protocol

2020 ◽  
Vol 25 (4) ◽  
pp. 4-9
Author(s):  
Yerzhan R. Baissalov ◽  
Ulan Dauyl
Keyword(s):  
Finite Fields ◽  
Matrix Algebras ◽  
Associative Structures

The article discusses primitive, linear three-pass protocols, as well as three-pass protocols on associative structures. The linear three-pass protocols over finite fields and the three-pass protocols based on matrix algebras are shown to be cryptographically weak.

Sign in / Sign up

Export Citation Format

Share Document