Keyword

function fields

Description: Function fields are fields of rational functions over a base field or associated with algebraic curves, studied in algebra and number theory.

Primary topic: Algebraic Geometry and Number Theory (53%)

OpenAlex ID: keywords/function-fields

Number Theory in Function Fields

2002 · Michael Rosen · Graduate texts in mathematics · 786

Introduction to Quadratic Forms over Fields

2004 · T.Y. Lam · Graduate studies in mathematics · 617

Chtoucas de Drinfeld et correspondance de Langlands

2002 · Laurent Lafforgue · Inventiones mathematicae · 325

The Theorem of Riemann-Roch for High Multiples of an Effective Divisor on an Algebraic Surface

1962 · Oscar Zariski · Annals of Mathematics · 279

Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil

1987 · Gérard Laumon · Publications mathématiques de l IHÉS · 263

Elliptic Modules

1974 · V G Drinfel'd · Mathematics of the USSR-Sbornik · 244

The Mordell-Lang conjecture for function fields

1996 · Ehud Hrushovski · Journal of the American Mathematical Society · 223

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Periods of Integrals on Algebraic Manifolds, I. (Construction and Properties of the Modular Varieties)

1968 · Phillip A. Griffiths · American Journal of Mathematics · 187

The second main theorem for small functions and related problems

2004 · Katsutoshi Yamanoi · Acta Mathematica · 178

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Valuations in Function Fields of Surfaces

1990 · Mark Spivakovsky · American Journal of Mathematics · 171

Imbedding of an abstract variety in a complete variety

1962 · Masayoshi Nagata · Kyoto journal of mathematics · 169

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Valuations and asymptotic invariants for sequences of ideals

2012 · Mattias Jonsson, Mircea Mustaţă · Annales de l’institut Fourier · 168

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Families of Algebraic Curves With Fixed Degeneracies

1971 · S J Arakelov · Mathematics of the USSR-Izvestiya · 168

Construction of Class Fields and Zeta Functions of Algebraic Curves

1967 · Goro Shimura · Annals of Mathematics · 168

Drinfeld Modular Curves

1986 · Ernst-Ulrich Gekeler · Lecture notes in mathematics · 153

The inverse Galois problem and rational points on moduli spaces

1991 · Michael D. Fried, Helmut V�lklein · Mathematische Annalen · 144

Formally p-adic Fields

1984 · Alexander Prestel, Peter Roquette · Lecture notes in mathematics · 144

Introduction to the theory of algebraic numbers and functions

1966 · Martin Eichler · 140

Algebraic Curves Over Function Fields. I

1968 · A N Paršin · Mathematics of the USSR-Izvestiya · 137

Sequences and their Applications

1999 · Ding, Cunsheng, Helleseth, T., et al. · Springer eBooks · 134

Jacobians of Drinfeld modular curves.

1996 · E.-U. Gekeler, M. REVERSAT · Journal für die reine und angewandte Mathematik (Crelles Journal) · 132

Twisted sheaves and the period-index problem

2008 · Max Lieblich · Compositio Mathematica · 127

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Über das verhalten der integrale 1. gattung bei automorphismen des funktionenkörpers

1934 · C. Chevalley, A. Weil, et al. · Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg · 127

Algebraic functions over finite fields

1967 · Harry Furstenberg · Journal of Algebra · 125

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Nested efficient congruencing and relatives of Vinogradov's mean value theorem

2018 · Trevor D. Wooley · Proceedings of the London Mathematical Society · 122

Works count: 4,580

Citation count: 30,930