# Download Algebraic Curves and One-Dimensional Fields by Fedor Bogomolov PDF

By Fedor Bogomolov

ISBN-10: 0821828622

ISBN-13: 9780821828625

Algebraic curves have many specified homes that make their learn rather profitable. for this reason, curves supply a common creation to algebraic geometry. during this ebook, the authors additionally deliver out features of curves which are distinct to them and emphasize connections with algebra. this article covers the basic themes within the geometry of algebraic curves, comparable to line bundles and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and primary cohomology teams. The authors make some degree of utilizing concrete examples and particular ways to make sure that the fashion is apparent and comprehensible. a number of chapters boost the connections among the geometry of algebraic curves and the algebra of one-dimensional fields. this can be an enticing subject that's hardly ever present in introductory texts on algebraic geometry. This e-book makes an outstanding textual content for a primary path for graduate scholars.

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Springer, 2004. 5. R. Blache, J. Estrada Sarlabous and M. Petkova. A geometric interpretation of reduction in the Jacobian of Cab curves. preprint. 6. C. Diem and E. Thom´e. Index calculus in class groups of non-hyperelliptic curves of genus three. accepted at J. of Cryptology, 2007. 7. E. W. Howe, K. E. Lauter and J. Top. Pointless curves of genus three and four. In Algebra, Geometry, and Coding Theory (AGCT 2003) (Y. Aubry and G. ), volume 11 of S´eminaires et Congr´es. Soci´et´e Math´ematique de France, Paris, 2005.

K. Khuri-Makdisi. Linear algebra algorithms for divisor on an algebraic curve. Math. of Computations, 73:333–357, 2004. 17. K. Khuri-Makdisi. asymptotically fast group operations on Jacobian of general curves. 2006. NT/0409209. 18. K. Miura and H. Yoshihara. Field theory for function fields of plane quartic curves. J. of Algebra, 226:283–294, 2000. February 11, 2008 28 15:6 WSPC - Proceedings Trim Size: 9in x 6in saga˙master S. Flon, R. Oyono, C. Ritzenthaler 19. E. Nart and C. Ritzenthaler. Non hyperelliptic curves of genus three over finite fields of characteristic two.

Math. of Computations, 73:333–357, 2004. 17. K. Khuri-Makdisi. asymptotically fast group operations on Jacobian of general curves. 2006. NT/0409209. 18. K. Miura and H. Yoshihara. Field theory for function fields of plane quartic curves. J. of Algebra, 226:283–294, 2000. February 11, 2008 28 15:6 WSPC - Proceedings Trim Size: 9in x 6in saga˙master S. Flon, R. Oyono, C. Ritzenthaler 19. E. Nart and C. Ritzenthaler. Non hyperelliptic curves of genus three over finite fields of characteristic two.