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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rational points and homogeneous spaces over function fields of curves
曲线函数场 有理点 齐次空间
2023/4/17
In the last decade, there has been a growing interest in the study of rational points on homogeneous spaces of linear algebraic groups defined over fields having good arithmetical properties other tha...
EXPLICIT CLASS FIELD THEORY FOR GLOBAL FUNCTION FIELDS
EXPLICIT CLASS FIELD THEORY GLOBAL FUNCTION FIELDS
2015/8/26
Let F be a global function field and let F ab be its maximal abelian extension. Following an approach of D. Hayes, we shall construct a continuous homomorphism ρ: Gal(F ab/F) → CF , where CF is the id...
Polyhedral Divisors, Dedekind Domains and Algebraic Function Fields
Polyhedral Divisors Dedekind Domains Algebraic Function Fields
2012/7/11
In this paper, we show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We describe also a class of multigraded a...
Representation of powers by polynomials over function fields and a problem of Logic
problem of Logic polynomials over function fields Number Theory
2011/9/15
Abstract: We solve a generalization of B\"uchi's problem in any exponent for function fields, and briefly discuss some consequences on undecidability. This provides the first example where this proble...
Degree three cohomology of function fields of surfaces
Degree three cohomology function fields of surfaces
2011/2/25
Let k be a global field or a local field. Class field theory says that every central division algebra over k is cyclic. If k contains lth roots of unity, for a prime l not equal to the characteristic ...
Let F be the function field of an elliptic curveX over Fq. In this paper, we calculate explicit formulas for unramified Hecke operators acting on automorphic forms over F. We determine these formulas ...
The space of toroidal automorphic forms was introduced by Zagier in 1979. Let F be a global field. An automorphic form on GL(2) is toroidal if it has vanishing constant Fourier coefficients along all ...
Computations in Cubic Function Fields of Characteristic Three
Computations Cubic Function Fields of Characteristic Three
2010/11/29
This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an int...