scholarly journals A remark on the decomposition of the Jacobian variety of Fermat curves of prime degree

2015 ◽  
Vol 105 (4) ◽  
pp. 333-341 ◽  
Author(s):  
Ruben A. Hidalgo ◽  
Rubí E. Rodríguez
Keyword(s):  
Jacobian Variety ◽  
Prime Degree ◽  
Fermat Curves

The group algebra decomposition of Fermat curves of prime degree

2015 ◽  
Vol 104 (2) ◽  
pp. 145-155 ◽  
Author(s):  
Patricio Barraza ◽  
Anita M. Rojas
Keyword(s):  
Group Algebra ◽  
Prime Degree ◽  
Fermat Curves ◽  
Group Algebra Decomposition

JACOBIAN VARIETY OF GENERALIZED FERMAT CURVES

2016 ◽  
Vol 67 (2) ◽  
pp. 261-284 ◽  
Author(s):  
Mariela Carvacho ◽  
Rubén A. Hidalgo ◽  
Saúl Quispe
Keyword(s):  
Jacobian Variety ◽  
Fermat Curves

scholarly journals On the symmetric determinantal representations of the Fermat curves of prime degree

2016 ◽  
Vol 12 (04) ◽  
pp. 955-967 ◽  
Author(s):  
Yasuhiro Ishitsuka ◽  
Tetsushi Ito
Keyword(s):  
Plane Curves ◽  
Symmetric Matrices ◽  
Torsion Points ◽  
Prime Degree ◽  
Linear Forms ◽  
Jacobian Varieties ◽  
Smooth Plane ◽  
Fermat Curves ◽  
Theta Characteristics

We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables with rational coefficients. In the proof, we use a relation between symmetric matrices with entries in linear forms and non-effective theta characteristics on smooth plane curves. We also use some results of Gross–Rohrlich on the rational torsion points on the Jacobian varieties of the Fermat curves of prime degree.

scholarly journals On Unramified Separable Abelian p-Extensions of Function Fields I

1959 ◽  
Vol 14 ◽  
pp. 223-234 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Galois Group ◽  
Function Field ◽  
Function Fields ◽  
Abelian Extension ◽  
Closed Field ◽  
Jacobian Variety ◽  
Algebraically Closed Field

Let k be an algebraically closed field of characteristic p>0. Let K/k be a function field of one variable and L/K be an unramified separable abelian extension of degree pr over K. The galois automorphisms ε1, …, εpr of L/K are naturally extended to automorphisms η(ε1), … , η(εpr) of the jacobian variety JL of L/k. If we take a svstem of p-adic coordinates on JL, we get a representation {Mp(η(εv))} of the galois group G(L/K) of L/K over p-adic integers.

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

scholarly journals Motivic decomposition of compactifications of certain group varieties

2018 ◽  
Vol 2018 (745) ◽  
pp. 41-58
Author(s):  
Nikita A. Karpenko ◽  
Alexander S. Merkurjev
Keyword(s):  
Central Simple Algebra ◽  
Simple Algebra ◽  
Chow Ring ◽  
Prime Degree ◽  
Central Simple

Abstract Let D be a central simple algebra of prime degree over a field and let E be an {\operatorname{\mathbf{SL}}_{1}(D)} -torsor. We determine the complete motivic decomposition of certain compactifications of E. We also compute the Chow ring of E.

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