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Class Numbers of Ray Class Fields of Imaginary Quadratic Fields
Elliptic curves Quadratic fields Ray class fields Imaginary quadratic fields
2014/12/8
Let K be an imaginary quadratic field with class number one and let [Special characters omitted.] be a degree one prime ideal of norm p not dividing 6 d K . In this thesis we generalize an algorithm o...
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...
Constructing higher dimensional local fields
Constructing higher dimensional local fields Algebraic Geometry
2012/4/18
This note is a gentle introduction to higher dimensional local fields, with the motivating problem being the standard geometric "localisation-completion" process by which they can be constructed. A di...
On Rees algebras and invariants for singularities over perfect fields
Rees algebras Integral closure Singularities Commutative Algebra
2011/8/31
Abstract: This purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations i...
Arithmetic of 0-cycles on varieties defined over number fields
zero-cycles Hasse principle weak approximation Brauer-Manin obstruction rationally connected varieties homogeneous spaces
2011/8/30
Abstract: Let $X$ be a rationally connected algebraic variety, defined over a number field $k$. We find a relation between the arithmetic of rational points on $X$ and the arithmetic of zero-cycles. M...
On the tensor rank of multiplication in finite extensions of finite fields
finite fields tensor rank of multiplication Algebraic Geometry
2011/8/26
Abstract: In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite fields and we establish new asymptotical and not asymptotical upper bounds abo...
In 70's there was discovered a construction how to attach to some algebraic-geometric data an infinite-dimensional subspace in the space k((z)) of the Laurent power series. The construction is known a...