Geometry of twisting cochains
We prove the existence of global minimal models for endomorphisms of projective space defined over the field of fractions of a principal ideal domain.
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.
The webs have been studied mainly locally, near regular points (see a short list of references on the topic in the bibliography). Let d be an integer ≥ 1. A d-web on an open set U of ℂ² is a differential equation F(x,y,y’) = 0 with , where the coefficients are holomorphic functions, a₀ being not identically zero. A regular point is a point (x,y) where the d roots in y’ are distinct (near such a point, we have locally d foliations mutually transverse to each other, and caustics appear through...
The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application...