![]() ![]() For example, IMHO the Bosch book is poor on cohomology theory, so I studied cohomology from FOAG Görtz and Wedhorn's book is poor on commutative algebra Eisenbud and Harris's book is rich with examples, but less so compared to FOAG Mumford's book does not contain exercises e.o. You can use FOAG for some more detailed study as these books complement it well. Despite it developing the theory through elementary methods, you can still find problems involving concrete curves that I think you will find interesting. Mumford - The Red Book of Varieties and Schemes I am not certain of what type of problems you want so I included Fulton which is an elementary introduction to classical algebraic geometry (no schemes).Görtz and Wedhorn - Algebraic Geometry I,.Gathmann's lecture notes ( Classical Algebraic Geometry and Scheme Theory),.Eisenbud and Harris - The Geometry of Schemes,.Bosch - Algebraic Geometry and Commutative Algebra,.A great part of the paper is devoted to preliminary technical. In the opinion of someone who has studied it, the essence of Hartshorne's book is in the exercises, and the exposition of the theory is not very clear (for obvious reasons).Īfter all this, my recommendation is that you continue your study of algebraic geometry from another textbook I suggest: These lectures give a detailed and almost self-contained introduction to algebraic stacks. On the other hand, the Harthshorne book (I write about his "Algebraic Geometry", with emphasis on Chapters II and III) is an underload of information because it recaps Éléments de géométrie algébrique by Grothendieck and Dieudonné (which is exactly 1800 pages of scheme theory, not a page more, not a page less), it is not very easy to read. In my humble opinion, the Vakil notes (also known as FOAG) are very complete with regards to scheme theory they include all prerequisites (category theory, commutative algebra, topology, etcetera omissis ) to scheme theory, an extensive bibliography, and also information about the "art status" of algebraic geometry.īut this completeness is an overload of information, so I use FOAG only for when I want a detailed study of some argument. Should I look up a solution after maybe struggling for half hour? There are solutions for Hartshorne, so maybe study Hartshorne is more convenient since it is easier to look up solution?Īlso, what is the right pace to learn the stuff? I mean should I worry if every day I spend $3$ hours to learn the stuff but I only finish $1$ page? (I know maybe I should spend more time, but unfortunately I am teaching myself algebraic geometry and I have other classes currently) How long should I spend for an exercise that stick me. ![]() So maybe I should try to work Hartshorne?Īnother question is about exercises. Hartshorne has notes on projective geometry which are available online and which I found quite useful. Dear Brandon, here are some MO links you could visit talking about Abundances conjecture: let me just suggest you that if youve just started algebraic geometry you should first gain familiarity with birational geometry, like Debarres, Kollàr and Moriss texts, before even understanding the statement of the conjecture. But the book has almost $800$ pages! Hartshorne has some proof, the exercises also have some explanation. I found projective geometry confusing when I began learning algebraic geometry. The typical situation is after $2$ hours work, maybe I am still in the same page. But the problem is most arguments are given in the form of exercises, which means I am always stuck. Abstract: This is an expository article on the theory of algebraic stacks. Especially, the exercises appear just in the right time, and there are more explanation of the exercises, so that I know what I am doing. I have worked through the first $4$ chapters of Vakil's notes and now I am thinking whether should I continue or try to study Hartshorne. In these two contexts, called respectively Complicial and Brave New Algebraic Geometry, we give some examples of geometric stacks such as the stack of associative dg-algebras, the stack of dg-categories, and a geometric stack constructed using topological modular forms.I believe Hartshorne and Vakil's notes are two most popular text currently, so my question is about how to choose the text. We then use the theory of stacks over model categories introduced in \cite the model category of symmetric spectra. a text book on algebraic stacks and the algebraic geometry that is needed to. We start by defining and studying generalizations of standard notions of linear and commutative algebra in an abstract monoidal model category, such as derivations, etale and smooth maps, flat and projective modules, etc. Contribute to stacks/stacks-project development by creating an account on. This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry.
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