Nash functions over real spectra
نویسندگان
چکیده
منابع مشابه
Affine Nash groups over real closed fields
We prove that a semialgebraically connected affine Nash group over a real closed field R is Nash isogenous to the semialgebraically connected component of the group H(R) of R-points of some algebraic group H defined over R. In the case when R = R this result was claimed in [5], but a mistake in the proof was recently found, and the new proof we obtained has the advantage of being valid over an ...
متن کاملReal Semigroups, Real Spectra and Quadratic Forms over Rings
real spectrum (ARS)finitely closed subset of, 52morphism of, 31projective limits of, 31residue space of, 66–69saturated subset of, 56subspace of, 61algebraLukasiewicz, 84Kleene, 87Post, 84AOSclosed subset, 210dependent subset, 210AOS-fan, 166archimedean-equivalent, 188ARS-fan, 170connected components, 208finiteisomorphi...
متن کاملGlobal Problems on Nash Functions
This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts, from manifolds over the reals to real spectra of arbitrary commutative rings. Nash functio...
متن کاملTheta Functions of Indefinite Quadratic Forms over Real Number Fields
We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.
متن کاملNash Manifolds and Schwartz Functions on Them
These are the lecture notes for my talk on December 1, 2014 at the BIRS workshop “Motivic Integration, Orbital Integrals, and Zeta-Functions”. 1. Semi-algebraic sets and the Seidenberg-Tarski theorem In this section we follow [BCR]. Definition 1.1. A subset A ⊂ R is called a semi-algebraic set if it can be presented as a finite union of sets defined by a finite number of polynomial equalities a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1989
ISSN: 0022-4049
DOI: 10.1016/0022-4049(89)90161-8