New PDF release: Algebraic Curves over Finite Fields

By Carlos Moreno

ISBN-10: 052134252X

ISBN-13: 9780521342520

During this tract, Professor Moreno develops the idea of algebraic curves over finite fields, their zeta and L-functions, and, for the 1st time, the idea of algebraic geometric Goppa codes on algebraic curves. one of the purposes thought of are: the matter of counting the variety of ideas of equations over finite fields; Bombieri's facts of the Reimann speculation for functionality fields, with outcomes for the estimation of exponential sums in a single variable; Goppa's thought of error-correcting codes created from linear structures on algebraic curves; there's additionally a brand new evidence of the TsfasmanSHVladutSHZink theorem. the must haves had to stick with this booklet are few, and it may be used for graduate classes for arithmetic scholars. electric engineers who have to comprehend the fashionable advancements within the idea of error-correcting codes also will take advantage of learning this paintings.

Show description

Read Online or Download Algebraic Curves over Finite Fields PDF

Best algebraic geometry books

Get Algebraic spaces PDF

Those notes are in accordance with lectures given at Yale college within the spring of 1969. Their item is to teach how algebraic services can be utilized systematically to improve convinced notions of algebraic geometry,which are typically handled via rational features by utilizing projective tools. the worldwide constitution that is usual during this context is that of an algebraic space—a area received by means of gluing jointly sheets of affine schemes via algebraic features.

Download e-book for kindle: Topological Methods in Algebraic Geometry by Friedrich Hirzebruch

In recent times new topological tools, particularly the speculation of sheaves based by means of J. LERAY, were utilized effectively to algebraic geometry and to the idea of capabilities of numerous advanced variables. H. CARTAN and J. -P. SERRE have proven how primary theorems on holomorphically whole manifolds (STEIN manifolds) will be for­ mulated by way of sheaf idea.

Get Introduction to Intersection Theory in Algebraic Geometry PDF

This ebook introduces a number of the major principles of recent intersection conception, lines their origins in classical geometry and sketches a number of common functions. It calls for little technical heritage: a lot of the fabric is on the market to graduate scholars in arithmetic. A large survey, the ebook touches on many issues, most significantly introducing a strong new technique constructed through the writer and R.

Rational Points on Curves over Finite Fields: Theory and by Harald Niederreiter PDF

Rational issues on algebraic curves over finite fields is a key subject for algebraic geometers and coding theorists. the following, the authors relate a massive program of such curves, particularly, to the development of low-discrepancy sequences, wanted for numerical tools in varied parts. They sum up the theoretical paintings on algebraic curves over finite fields with many rational issues and talk about the functions of such curves to algebraic coding thought and the development of low-discrepancy sequences.

Additional info for Algebraic Curves over Finite Fields

Sample text

For notational convenience we let Oi /t (D) = Homk(A/(A(D) + K),k); we observe that if the divisors D, D' satisfy D < D', then &Klk(D') £ ClsK/k(D). Hence we can view the space of pseudo-differentials on K as a projective limit ci"m = lim arKlk(D). 8 Let 0 denote the zero divisor of K; the space QsK/k(&) is called the space of pseudo-differentials of the first kind. °Klk(D) = S(D). e. dimkn*Klk(<9) = g. We now want to show that Q^ /t (also known as the dualizing module) may also be viewed as a vector space over K.

In fact if this were not the case then we could represent 1 in the form 1 = j ^ y , + ••• + xhyh, with x, e mA, y{ e AY (1 <. i < h). Each yt would belong to some ring A(i) e &'. For each pair (i,j) one of the rings Am, AU) would contain the other; since there are only a finite number of rings A(i), it follows that they would all be contained in one of them, say A{k). But then we would have 1 = £ ? ^ e mA • A(k\ therefore mA • A{k) = Alk\ which is impossible since Aik) e &'. ¥, and hence 3F is inductive.

Any element x e RQ has a representation of the form d x = X a/*; + *'> J=l with x' e WIQ. , d and all P e S, we obtain ordP(ux,) + ordP(D + Q) > 0; hence MX, e L(D + Q)s. An element x e L(D + Q)s satisfies ord e (X) + ord e (D + Q) > 0 and hence ordQ(xu~x) = ordQ(x) — ordQ(u) = ord e (u) + ord e (D + Q) > 0, that is to say xu'1 e RQ; therefore we have d XM"1 = X aJxJ + x'> j=l with aj e k and x' e mQ. , d and all PeS - {Q} it follows that ord P (x') > 0 and therefore ord P (ux') + ordP(D) = ordP(wx') + ord P (D + Q) > 0 for all P e S - {Q}.

Download PDF sample

Algebraic Curves over Finite Fields by Carlos Moreno

by Joseph

Rated 4.11 of 5 – based on 6 votes