Purely inseparable points on curves

Hopf Galois structures on primitive purely inseparable extensions

Let L/K be a primitive purely inseparable extension of fields of characteristic p, [L : K] > p, p odd. It is well known that L/K is Hopf Galois for some Hopf algebra H, and it is suspected that L/K is Hopf Galois for numerous choices of H. We construct a family of K-Hopf algebras H for which L is an H-Galois object. For some choices of K we will exhibit an infinite number of such H. We provide ...

Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

Follow up what we will offer in this article about pythagorean hodograph curves algebra and geometry inseparable. You know really that this book is coming as the best seller book today. So, when you are really a good reader or you're fans of the author, it does will be funny if you don't have this book. It means that you have to get this book. For you who are starting to learn about something n...

Cartier Points on Curves

Throughout this paper Y will denote a complete, nonsingular, and irreducible algebraic curve of genus g > 0 over the algebraically closed field k of characteristic p. Eventually we will assume that g ≥ 2. Denote by W the g-dimensional k-vector space of regular differentials of Y/k, which is just the vector space H(Y,ΩY/k). Also let K(Y ) denote the function field of Y , and let ΩK(Y )/k be the ...

Rational points on curves

Rational points on curves

2 Faltings’ theorem 15 2.1 Prelude: the Shafarevich problem . . . . . . . . . . . . . . . . 15 2.2 First reduction: the Kodaira–Parshin trick . . . . . . . . . . . 17 2.3 Second reduction: passing to the jacobian . . . . . . . . . . . 19 2.4 Third reduction: passing to isogeny classes . . . . . . . . . . . 19 2.5 Fourth reduction: from isogeny classes to `-adic representations 21 2.6 The isogen...