This book uses algebraic tools to study the elementary properties
of classes of fields and related algorithmic problems. The first
part covers foundational material on infinite Galois theory,
profinite groups, algebraic function fields in one variable and
plane curves. It provides complete and elementary proofs of the
Chebotarev density theorem and the Riemann hypothesis for function
fields, together with material on ultraproducts, decision
procedures, the elementary theory of algebraically closed fields,
undecidability and nonstandard model theory, including a
nonstandard proof of Hilbert's irreducibility theorem. The focus
then turns to the study of pseudo algebraically closed (PAC)
fields, related structures and associated decidability and
undecidability results. PAC fields (fields K with the property that
every absolutely irreducible variety over K has a rational point)
first arose in the elementary theory of finite fields and have deep
connections with number theory. This fourth edition substantially
extends, updates and clarifies the previous editions of this
celebrated book, and includes a new chapter on Hilbertian subfields
of Galois extensions. Almost every chapter concludes with a set of
exercises and bibliographical notes. An appendix presents a
selection of open research problems. Drawing from a wide literature
at the interface of logic and arithmetic, this detailed and
self-contained text can serve both as a textbook for graduate
courses and as an invaluable reference for seasoned researchers.
General
| Imprint: |
Springer International Publishing AG
|
| Country of origin: |
Switzerland |
| Series: |
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11 |
| Release date: |
June 2023 |
| First published: |
2023 |
| Authors: |
Michael D. Fried
• Moshe Jarden
|
| Dimensions: |
235 x 155mm (L x W) |
| Pages: |
827 |
| Edition: |
4th ed. 2023 |
| ISBN-13: |
978-3-03-128019-1 |
| Categories: |
Books
Promotions
|
| LSN: |
3-03-128019-9 |
| Barcode: |
9783031280191 |
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