Algebraic Geometry

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From the reviews

"All of Weil’s works aside from books and lecture notes are compiled the following, in strict chronological order for simple reference.

But the price … is going past the benefit of straightforward reference and accessibility. within the first position, those volumes comprise a number of essays, letters, and addresses that have been both released in vague locations (…) or no longer released in any respect.

Even extra precious are the long commentaries on some of the articles, written via Weil himself. those comments function a advisor, aiding the reader position the papers of their right context. additionally, we now have the infrequent chance of seeing a good mathematician in his later existence reflecting at the improvement of his principles and people of his contemporaries at quite a few phases of his career.

The sheer variety of mathematical papers of basic value may earn Weil’s gathered Papers a spot within the library of a mathematician with an curiosity in quantity idea, algebraic geometry, representations concept, or comparable components. the extra import of the mathematical heritage and tradition in those volumes makes them much more essential." Neal Koblitz in Mathematical Reviews

"André Weil’s mathematical paintings has deeply stimulated the math of the 20 th century and the enormous (...) "Collected papers" emphasize this influence." O. Fomenko in Zentralblatt der Mathematik

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Read or Download Oeuvres Scientifiques / Collected Papers: Volume 3 (1964-1978) PDF

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The speculation of elliptic curves is unique by way of its lengthy historical past and through the variety of the equipment which have been utilized in its research. This ebook treats the mathematics technique in its smooth formula, by utilizing simple algebraic quantity idea and algebraic geometry. Following a quick dialogue of the mandatory algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the advanced numbers, neighborhood fields, and worldwide fields.

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This ebook introduces the speculation of modular varieties, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner conception; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms.

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