An introduction to locally compact abelian algebraic groups and the usage of dual groups and Fourier transforms to study them.

There is a natural analytification functor from the category of locally separated algebraic spaces locally of finite type over C to the category of complex-analytic spaces [Kn, Ch. I, 5.17ff]. (Recall that a map of algebraic spaces X → S is locally separated if the diagonal ∆X/S : X → X ×S X is an immersion. We require algebraic spaces to have quasi-compact diagonal over SpecZ.) It is natural t...

This paper is concerned with the algebraic K-theory of locally convex C-algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that if L is locally convex and J a Fréchet operator ideal, then all the different variants of topological K-theory agree on the completed projective tensor product L⊗̂J , and that the obstruction for the comparison map K(L⊗̂J ) → K(...

Arithmetic groups are fundamental groups of locally symmetric spaces. We will see how they are constructed, and discuss some of their important properties. For example, although the Q-rank of an arithmetic group is usually defined in purely algebraic terms, we will see that it provides important information about the geometry and topology of the corresponding locally symmetric space. Algebraic ...

1 Abbreviations and Notations 3 1 General Introduction 4 1.1 PCP theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Property Testing . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Locally Testable Codes . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Random locally testable codes . . . . . . . . . . . . . 6 1.3.2 Algebraic Construction of LTCs . . . . . . . . . . ....

In [Alcazar, J.G., Sendra, J.R. 2006. Local shape of offsets to rational algebraic curves. Tech. Report SFB 2006-22 (RICAM, Austria); Alcazar, J.G., Sendra, J.R. 2007. Local shape of offsets to algebraic curves. Journal of Symbolic Computation 42, 338–351], the notion of good local behavior of an offset to an algebraic curve was introduced to mean that the topological behavior of the offset cur...

We characterize of the Bernstein-Bezier (BB) form of an implicitly deened bivariate polynomial over a triangle, such that the zero contour of the polynomial deenes a smooth and single sheeted real algebraic curve segment. We call a piecewise G k-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree n A-splines can...

We characterize those maps between homotopically stratified spaces whose mapping cylinders are also homotopically stratified spaces. Two applications are offered. The first concerns locally flat submanifolds of topological manifolds, and the second concerns algebraic maps between algebraic varieties.  1999 Elsevier Science B.V. All rights reserved.

We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is étale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin’s algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.

A necessary algebraic condition is obtained for the intrinsic geometry of any spacetime locally and isometrically embedded into a pseudo-Euclidean 5-space.