Naive Introduction to Algebraic Geometry: the Geometry of Rings
ثبت نشده
چکیده
I. BASIC TOOL: RATIONAL PARAMETRIZATION Algebraic geometry is a generalization of analytic geometry the familiar study of lines, planes, circles, parabolas, ellipses, hyperbolas, and their 3 dimensional versions: spheres, cones, hyperboloids, ellipsoids, and hyperbolic surfaces. The essential common property these all have is that they are defined by polynomials. This is the defining characteristic of classical algebraic sets, or varieties they are loci of polynomial equations.
منابع مشابه
The Geometry of Formal Varieties in Algebraic Topology I
Algebraic topology is full of computations with rings, and where we find rings we should seek geometry through methods of algebraic geometry. The geometry of formal varieties turn out to organize many interesting computations in topology, and certain formal varieties called commutative, one-dimensional formal groups give the best global picture of stable homotopy theory currently available. I w...
متن کاملConvex Extensions of Partially Ordered Rings
This series of lectures is about algebraic aspects of real algebraic geometry. Partially ordered rings (porings) occur very naturally in real algebraic geometry, as well as in other branches of mathematics. There is a rich classical theory of porings (the beginnings dating back to the 1930s and 1940s). To a large extent it was inspired by the study of rings of continuous functions in analysis a...
متن کاملFormal and Rigid Geometry: an Intuitive Introduction, and Some Applications
We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory, with special emphasis on recent applications to the Milnor fibration and the motivic zeta function by J. Sebag and the author.
متن کاملΛ-rings and the Field with One Element
The theory of Λ-rings, in the sense of Grothendieck’s Riemann– Roch theory, is an enrichment of the theory of commutative rings. In the same way, we can enrich usual algebraic geometry over the ring Z of integers to produce Λ-algebraic geometry. We show that Λ-algebraic geometry is in a precise sense an algebraic geometry over a deeper base than Z and that it has many properties predicted for a...
متن کاملOrderings for Noncommutative Rings
Introduction and Notation. The goal of this paper is to present the beginnings of a theory of real algebraic geometry for noncommutative rings. For a basic introduction to the commutative theory, see Lam [L]. The word field will be used in this paper to mean a (generally noncommutative) skewfield; we shall specify a commutative field when we need to. R will denote a noncommutative ring with 1. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007