![]() Maybe if one is a beginner then a clear introductory book is enough or if algebraic geometry is not ones major field of study then a self-contained reference dealing with the important topics thoroughly is enough. Geometry', Oxford University Press, Oxford, 2006.I think Algebraic Geometry is too broad a subject to choose only one book. Huybrechts, 'Fourier-Mukai transforms in Algebraic Thomas, 'Derived categories for the working und ihrer Grenzgebiete 39, Springer-Verlag, Berlin, 2000. Moret-Bailly, 'Champs algebriques', Ergeb.ĭer Math. Publications 62, A.M.S., Providence, RI, 2016. Olsson, 'Algebraic Spaces and Stacks', A.M.S. Hartshorne, 'Algebraic Geometry', Graduate Texts in Math. Vezzosi, 'From HAG to DAG: derived moduli Vezzosi, ‘Homotopical Algebraic Geometry II: Geometric Geometry V: Structured spaces’, arXiv:0905.0459. Toën, 'Higher and derived stacks: a global overview', math.AG/0604504. Bibliography: Useful survey papers on DAG: Pantev-Toën-Vaquié-Vezzosi, and applications to Donaldson-Thomas theory ofĬalabi-Yau 3- and 4-folds. Lecture 14: Shifted symplectic derived stacks, following Sense of stability conditions on abelian categories, and in Geometric Invariant Semi-classical shadow of a quasi-smooth derived stack. To Derived Algebraic Geometry: a classical stack with obstruction theory is the How they are used to define enumerative invariants. Theories and virtual classes on classical schemes and stacks, followingīehrend-Fantechi. Gromov-Witten invariants, algebraic Donaldson invariants). Lecture 13: Enumerative invariants in Algebraic Geometry Cotangent complexes of derived schemes and Lecture 12: The definitions of derived schemes and derived Segal categories.įoundational theories of DAG in the literature. Lecture 11: Stable ∞-categories as the "correct"ĭefinition of triangulated category. Lecture 9: Informal introduction to ∞-categories. Derived categories of coherent sheaves D bcoh(X). Lecture 8: More on triangulated categories and derivedĬategories. Lecture 7: Introduction to derived categories and The classifying stack of principal bundles. Lecture 4: Global quotient stacks, as a way of introducingĭeligne-Mumford and Artin stacks before giving the formal definition, andĮmphasizing the 2-categorical aspects. Need higher categories in derived geometry. Fibre products in ordinary categories why we Commutative differential graded algebras, examples.īézout’s Theorem and derived Bézout’s Theorem. Moduli spaces as ‘representable functors’.ĭerived schemes and stacks. Schemes as functorsĪlg K → Sets, and stacks as functors Alg K → Groupoids. Of category theory, categories, functors. In algebraic geometry: schemes, stacks, higher stacks, derived stacks. I can probably teach you how to bluff about DAG at parties, though. So if youĪsk me technical questions about the fppf topology, etc, I won't know theĪnswer. Without actually spending two years reading Lurie and Toën-Vezzosi. I've mostly picked the subject up by osmosis, Geometry, which were developed much earlier than DAG), and ∞-categories,īefore trying to explain derived schemes and derived stacks at the end of the Several weeks talking about other stuff which is interesting for its own sake:Ĭlassical stacks, triangulated categories and derived categories (derivedĬategories are a necessary prequel to derived stacks and derived algebraic Part of theĭifficulty is that the theory must be set in the world ofĪfter a brief discussion of derived geometry in the first week, I will spend Papers, due to Lurie and Toën-Vezzosi, run to 1000's of pages. The richer geometric structure on the derived stack Mĭerived Algebraic Geometry is famously hard to learn - the foundational A coherent sheafĮ in coh(X) corresponds to points in M andĮxt i( E, E) for i=0,1, but the derived cotangentĮxt i( E, E) for all i=0,1., m. Then we canįorm the classical moduli stack M and the derived moduli stack X be a smooth projective scheme of dimension m. In moduli spaces of objects in Calabi-Yau categories. Important in problems involving virtual classes and enumerative invariants, and These are enhanced versions of classical schemes and (Artin) stacks Synopses:ĭerived Algebraic Geometry is the study of "derived" schemes and "derived" Teams link, you can only get into the Teams meeting if your e-mail address hasīeen authorized by the TCC staff. I am sorry, but if you are not at one of these five universities, you can'tĬome to the course. ![]() This course is put on by the Taught Course Centre, and willīe transmitted to the Universities of Bath, Bristol, Oxford, Warwick and Professor Joyce Derived Algebraic Geometry Fridays 2pm - 4pm on MS Teams, starting on 29th April and finishing on 17th Derived Algebraic Geometry - Prof Joyce - TT Graduate lecture course, 14 lectures, Summer Term 2022.
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