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ORTHOGONAL INVOLUTIONS ON CENTRAL SIMPLE ALGEBRAS AND FUNCTION FIELDS OF SEVERI-BRAUER VARIETIES [PDF]

Advances in Mathematics, 2018
An orthogonal involution $ $ on a central simple algebra $A$, after scalar extension to the function field $\mathcal{F}(A)$ of the Severi--Brauer variety of $A$, is adjoint to a quadratic form $q_ $ over $\mathcal{F}(A)$, which is uniquely defined up to a scalar factor.
Anne Quéguiner-Mathieu, Jean-Pierre Tignol   +1 more
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L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields [PDF]

Inventiones mathematicae, 2006
To appear in Inventiones ...
Douglas Ulmer
openalex   +5 more sources

Partial Zeta Functions of Algebraic Varieties over Finite Fields

Finite Fields and Their Applications, 2001
By restricting the variables running over various (possibly different) subfields, we introduce the notion of a partial zeta function. We prove that the partial zeta function is rational in an interesting case, generalizing Dwork's well known rationality theorem. In general, the partial zeta function is probably not rational.
Daqing Wan
openalex   +6 more sources

Appell-Lauricella hypergeometric functions over finite fields and algebraic varieties [PDF]

Hokkaido Mathematical Journal
26 ...
A. Nakagawa
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Parametric Expansions of an Algebraic Variety Near Its Singularities II

Axioms
The paper is a continuation and completion of the paper Bruno, A.D.; Azimov, A.A. Parametric Expansions of an Algebraic Variety Near Its Singularities.
Alexander D. Bruno, Alijon A. Azimov
doaj   +2 more sources

Algebraic varieties and function fields over a finite field

, 2002
Nous nous intéressons au nombre de points rationnels des variétés algébriques projectives sur un corps fini. Nous déterminons notamment la fonction zêta (et plus précisément les polynômes caractéristiques de l'endomorphisme de Frobenius sur les espaces de cohomologie étale l-adique) des courbes algébriques projectives sans autre hypothèse de lissité ou
Yves Aubry
openalex   +3 more sources

On the endomorphism algebra of Jacobian varieties attached to the fields of elliptic modular functions

Osaka Journal of Mathematics, 1964
Tokuji Matsui
openalex   +4 more sources

IwasawaL-functions of varieties over algebraic number fields

Inventiones Mathematicae, 1983
Peter Schneider
openalex   +3 more sources

Differential Function Fields and Moduli of Algebraic Varieties [PDF]

, 1986
Alexandru Buium
openalex   +2 more sources

On rank in algebraic closure [PDF]

Selecta Mathematica, 2022
Let $ {\mathbf k} $ be a field and $Q\in {\mathbf k}[x_1, \ldots, x_s]$ a form (homogeneous polynomial) of degree $d>1.$ The ${\mathbf k}$-Schmidt rank $rk_{\mathbf k}(Q)$ of $Q$ is the minimal $r$ such that $Q= \sum_{i=1}^r R_iS_i$ with $R_i, S_i \in ...
Amichai Lampert, T. Ziegler
semanticscholar   +1 more source