| Session | Day | Speaker | Content |
|---|---|---|---|
| Session 1 | Friday April 26, 4 pm | Sara Mehidi | Chapter 1 & 2: Background (1/2): Motivation for studying stacks, Grothendieck topologies, sites, projective limits, étale/fppf sheaves, topos and morphisms of topos. Notes. |
| Session 2 | Monday April 29, 5 pm | Amira Tlemsani | Chapter 1 & 2: Background (2/2): Continuous functors between topos, when to lift a continuous functor between sites into a functor in the induced topos, representable functors are sheaves for the fppf topology. |
| Session 3 | Friday May 3, 3 pm | Zakaria Ouaras | Chapter 3: Fibered categories (1/2): Cartesian maps, fibered categories, the 2-Yoneda lemma, categories fibered in sets (the 1-Yoneda lemma), the category of presheaves is equivalent to that of fibered categories in sets. |
| Session 4 | Monday May 13, 3 pm | Sara Mehidi | Chapter 3 (2/2): Cleavage in a fibered category, splitting fibered categories, groupoids, categories fibered in groupoids. Notes. |
| Session 5 | Wednesday May 22, 3 pm | Amira Tlemsani | Chapter 4: Descent and the stack condition (1/2): Faithfully flat descent, generalities on descent, example: a morphism with a section is an effective descent morphism. |
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| Session 6 | Monday May 27, 3 pm | Zakaria Ouaras | Chapter 4 (2/2): More examples of effective descent morphisms (closed subschemes, open embeddings, affine morphisms, polarized schemes, M_g), prestacks and stacks, stackification, fiber product of stacks. Notes |
| Session 7 | Thursday June 06, 3 pm | Sara Mehidi | Chapter 5: Algebraic spaces (1/2): Representable morphisms of sheaves, definition of an algebraic space, étale equivalence relation, any algebraic space is the quotient of a scheme by an étale équivalence relation and conversely, example of an algebraic space: the quotient of a scheme by a discrete group acting freely. Notes. |
| Session 8 | Friday June 14, 3 pm | Amira Tlemsani & Céline Fietz | Chapter 5 (2/2): Examples of algebraic spaces which are not schemes, the quotient of an affine scheme by a finite étale equivalence relation is a scheme (eg. free action of a finite discrete group). Notes. Some properties of morphisms of algebraic spaces, quasi-separatedness/ separatedness/ quasi-compactness, algebraic spaces are fppf sheaves. Notes. |
| Session 9 | Monday June 24, 3 pm | Amira Tlemsani & Céline Fietz | Chapter 8: Algebraic stacks (1/2): Definition of algebraic stack and fiber products Notes, properties of algebraic stacks and morphisms between them Notes. |
| Session 10 | Friday June 28, 3 pm | Boaz Moerman | Chapter 8 (2/2): Deligne-Mumford stacks, examples. Notes. |
Organizers:
Sara Mehidi (University of Utrecht; s.mehidi[at]uu.nl);
Zakaria Ouaras (University of Nice; ouaras[at]unice.fr);
Amira Tlemsani (University of Leiden; a.tlemsani[at]math.leidenuniv.nl).