If you have never seen a prime ideal sheaf or a scheme before, pairing Liu with a more geometric introduction (like Görtz-Wedhorn or Eisenbud-Harris) is wise.
: Check your university library or any online catalogs like WorldCat to see if they have a digital or physical copy of the book.
The book is structured to build a scheme-theoretic foundation with a specific end goal: understanding arithmetic curves. While standard texts often use algebraically closed fields (like $\mathbb{C}$) as the base case, Liu embraces the difficulty of working over general rings, specifically Dedekind domains and eventually the ring of integers $\mathbb{Z}$.
While many students look for a version of Algebraic Geometry and Arithmetic Curves for quick reference or searchability, the book is a published volume in the Oxford Graduate Texts in Mathematics series (Volume 6).
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 you have never seen a prime ideal sheaf or a scheme before, pairing Liu with a more geometric introduction (like Görtz-Wedhorn or Eisenbud-Harris) is wise.
: Check your university library or any online catalogs like WorldCat to see if they have a digital or physical copy of the book. liu algebraic geometry and arithmetic curves pdf
The book is structured to build a scheme-theoretic foundation with a specific end goal: understanding arithmetic curves. While standard texts often use algebraically closed fields (like $\mathbb{C}$) as the base case, Liu embraces the difficulty of working over general rings, specifically Dedekind domains and eventually the ring of integers $\mathbb{Z}$. If you have never seen a prime ideal
While many students look for a version of Algebraic Geometry and Arithmetic Curves for quick reference or searchability, the book is a published volume in the Oxford Graduate Texts in Mathematics series (Volume 6). While standard texts often use algebraically closed fields
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.