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Introduction to the Theory of Algebraic Functions of One Variable
 
Introduction to the Theory of Algebraic Functions of One Variable
Softcover ISBN:  978-0-8218-1506-9
Product Code:  SURV/6
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1233-3
Product Code:  SURV/6.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1506-9
eBook: ISBN:  978-1-4704-1233-3
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
Introduction to the Theory of Algebraic Functions of One Variable
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Introduction to the Theory of Algebraic Functions of One Variable
Softcover ISBN:  978-0-8218-1506-9
Product Code:  SURV/6
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1233-3
Product Code:  SURV/6.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-1506-9
eBook ISBN:  978-1-4704-1233-3
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 Details
     
     
    Mathematical Surveys and Monographs
    Volume: 61951; 188 pp
    MSC: 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 Riemann-Roch
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 61951; 188 pp
MSC: 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.

  • Chapters
  • I. Places and divisors
  • II. The theorem of Riemann-Roch
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.