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Finite Fields Algebraic curves Rational Points Weierstrass Points Function fields genus towers of function fields Rational places maximal curves Drinfeld-Vladut bound towers of curves Corpos Finitos Algebraic Function Fields prime characteristic pontos racionais Curvas Algebricas Artin-Schreier extensions Coverings Of Curves Hasse-Weil bound limit of towers curvas maximais cota de Hasse-Weil Goppa codes genus of curves minimum distance Osculating Spaces Hermitian curve Artin-Schreier covers asymptotic behaviour Fermat curves Abelian Extensions limits of towers Grupos Finitos Hasse-Weil upper bound Weierstrass gaps cota de Drinfeld-Vladut recursive towers Kummer covers Riemann Hypothesis Pontos de Weierstrass Automorphism Groups additive polynomials Abhyankar lemma cubic finite fields Order Sequences Hasse- Weil upper bound Gorenstein singularities intersection numbers Abhyankar's lemma semigroup of values galois closure genus of towers Weil's bound Artin-Schreier towers applications to coding theory Frobenius-orders cota de T.Zink Hermitian curves torres de corpos de funcoes Nonclassical Curves tame towers Explicit towers Aneis Fatoriais Gorenstein Rings Zink's bound symmetric polynomials Curves over Finite Fields Pesos de Weierstrass Singular Points Gap Sequences Recobrimentos de Curvas wild ramification constructions of curves limit of a tower Kummer Curves genus of function fields Semigroup Rings Frobenius orders Ramification Points higher order differentials Weirstrass Points Weil Upper Bound different exponents Giulietti-Korchmaros curve Gilbert-Varshamov bound on codes Zink lower bound Zink's lower bound Caracterizacao de Recobrimentos algebras de grupo Genero de Curvas Geradores e relacoes Aneis de Gorenstein Frobenius Morphism Dominios Euclidianos e Fatoriais Cohen-Macaulay rings plane curves Nodal Curves Conductors Composita Of Towers function field plane singular curves Gorenstein Curves Invariantes Topologicos Semigrupos de Singularidades idempotentes centrais Pontos de ramificacao Grupos Abelianos Grupos Abelianos Finitamente Gerados Cota de Serre Singularities Branches unibranch singularities Prime Characteristics Morphisms Of Curves Branches Of Curves Rational Curves Singularities Degrees Chebyshev polynomials finite field explicit constructions of curves intersection semigroups Pontos Singulares Equivalencia Topologica Realizacao de Semigrupos de Weierstrass lugares racionais algebras de semigrupo classificação de curvas maximais completamentos em corpos de funções Grupos Metaciclicos Singularidades de Curvas Hipotese de Riemann Modulos Finitamente Gerados Coding Theory Gorestein Singularities Semigroups Of Singularities Weierstrass Weights projective line Kummer Extensions Automorphisms Gauss Maps Singularities Of Curves Subrings In Function Fields rational place Duality for curves Dualizing sheaf branches at singularities Canonical Ideals consecutive gaps Stohr-Voloch's theory Semigrupos generos grupos nilpotentes curvas supersingulares Sequencia de lacunas Strange Curves unramified covers Teoremas de Sylow Teoremos de Sylow Cryptography Semigroups Equisingularity Wronskian Determinants fixed points duality Weirstrass Weights smooth points Integral Closure gaps finiteness of automorphisms canonical morphisms Drinfeld- Vladut upper bound Associated Cone Hasse- Weil bound invariants of towers Goopa Codes teorema de Weil torres de curvas tame ramification linear codes Jacobian variety Topological Invariants Associated graded ring Apery sequence Orders Of Morphisms Self Duality Riemann-Roch-Rosenlicht subcovers of Hermitian curve Deuring Polynomial Kummer and Artin-Schreier towers Galois covers Ore ring Higher ramification groups explicit equations Drinfeld - Vladut bound Upper Bounds Cohen-Macaulay Property tower of curves Tsfasman-Vladut- Zink bound galois closures Gauss map curvas de Fermat genus of fields graphs Galois coverings Hermitian function field Supersingular elliptic curves dual towers classification of recursive towers commutativity of additive polynomials Waring problem Asymptotic Goppa codes class field theory geometric Goppa codes Geometric codes applications to Goppa codes Zariski equisingularity Self-Duality Duality of Curves construcoes de curvas