Softcover ISBN:  9780821815069 
Product Code:  SURV/6 
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eBook ISBN:  9781470412333 
Product Code:  SURV/6.E 
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Softcover ISBN:  9780821815069 
eBook: ISBN:  9781470412333 
Product Code:  SURV/6.B 
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Softcover ISBN:  9780821815069 
Product Code:  SURV/6 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412333 
Product Code:  SURV/6.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821815069 
eBook ISBN:  9781470412333 
Product Code:  SURV/6.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 6; 1951; 188 ppMSC: Primary 14;
This classical book, written by a famous French mathematician in the early 1950s, presents an approach to algebraic geometry of curves treated as the theory of algebraic functions on the curve. Among other advantages of such an approach, it allowed the author to consider curves over an arbitrary ground field. Among topics discussed in the book are the theory of divisors on a curve, the Riemann–Roch theorem, \(p\)adic completion, extensions of the fields of functions (covering theory) and of the fields of constants, and the theory of differentials on a curve. The last chapter, which is more analytic in flavor, treats the theory of Riemann surfaces.
Prerequisites for reading are minimal and include only an advanced undergraduate algebra course.

Table of Contents

Chapters

I. Places and divisors

II. The theorem of RiemannRoch

III. The $\mathfrak {p}$adic completions

IV. Extensions of fields of algebraic functions of one variable

V. Extensions of the field of constants

VI. Exact differentials

VII. The Riemann surface


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This classical book, written by a famous French mathematician in the early 1950s, presents an approach to algebraic geometry of curves treated as the theory of algebraic functions on the curve. Among other advantages of such an approach, it allowed the author to consider curves over an arbitrary ground field. Among topics discussed in the book are the theory of divisors on a curve, the Riemann–Roch theorem, \(p\)adic completion, extensions of the fields of functions (covering theory) and of the fields of constants, and the theory of differentials on a curve. The last chapter, which is more analytic in flavor, treats the theory of Riemann surfaces.
Prerequisites for reading are minimal and include only an advanced undergraduate algebra course.

Chapters

I. Places and divisors

II. The theorem of RiemannRoch

III. The $\mathfrak {p}$adic completions

IV. Extensions of fields of algebraic functions of one variable

V. Extensions of the field of constants

VI. Exact differentials

VII. The Riemann surface