: Look for open-access platforms or digital libraries that might host the book. However, be aware that accessing copyrighted material without permission is illegal.
If Hartshorne is too fast, use Liu to see the details. If Liu feels too technical, use Hartshorne to get the "big picture" intuition. liu algebraic geometry and arithmetic curves pdf
How to find a "simplest" representative of a curve over a local field. : Look for open-access platforms or digital libraries
The specific text you might be looking for is "Algebraic Geometry and Arithmetic Curves" by Qing Liu. This book is a comprehensive treatment that covers fundamental aspects of algebraic geometry, with a focus on the arithmetic of curves. It serves as a valuable resource for students and researchers interested in understanding both the geometric and arithmetic aspects of curves. If Liu feels too technical, use Hartshorne to
As for the study of algebraic varieties, there are many other excellent (specific) textbooks that can be consulted. As stated befo... Google Books https://books.google.com Algebraic Geometry and Arithmetic Curves - Qing Liu This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of... Google Books https://books.google.com Algebraic Geometry and Arithmetic Curves - Qing Liu Qing Liu. Oxford University Press, 2002 - Mathematics - 576 pages. This book is a general introduction to the theory of schemes, f... Amazon UK https://www.amazon.co.uk Algebraic Geometry and Arithmetic Curves (Oxford Graduate Texts ... Top reviews from other countries * Zeyu. 5.0 out of 5 starsVerified Purchase. Nice companion to Hartshorne's algebraic geometry bo... Oxford University Press https://global.oup.com Algebraic Geometry and Arithmetic Curves - Hardcover Jul 18, 2002 —
The exercises are excellent. They are not just computational drills; many extend the theory, introduce counterexamples, or build toward important corollaries (e.g., proving the Riemann-Roch theorem for curves, or the finiteness of the class group of a number field).