We show that every Deligne-Mumford gerbe over a field occurs as the residual gerbe of a point of the moduli stack of curves. Informally, this means that the moduli space of curves fails to be a fine moduli space in every possible way. We also show the same result for a list of other natural moduli problems. This is joint work with Max Lieblich.
A Stacky Murphy’s Law for the Stack of Curves Sponsored by the Meyer Fund
Apr. 25, 2024 12:20pm (Math …
Noncomm Geometry
Dmitry Kaledin (Steklov Math Institute)
X
It has become accepted wisdom by now that when you localize a category with respect to a class of morphisms, what you get is not just a category but a category "with a homotopical enhancement". Typically, the latter is made precise through the machinery of "infinity-categories", or "quasicategories", but this is quite heavy technically and not really optimal from the conceptual point of view. I am going to sketch an alternative technique based on Grothendieck's idea of a "derivator".
How to enhance categories, and why Sponsored by the Meyer Fund
Apr. 25, 2024 12:20pm (MATH …
Algebraic Geometry
Dmitry Kaledin (Steklov Math Institute)
X
It has become accepted wisdom by now that when you localize a category with respect to a class of morphisms, what you get is not just a category but a category "with a homotopical enhancement". Typically, the latter is made precise through the machinery of "infinity-categories", or "quasicategories", but this is quite heavy technically and not really optimal from the conceptual point of view. I am going to sketch an alternative technique based on Grothendieck's idea of a "derivator".
How to enhance categories, and why (Cross listed with Non-commutative Geometry) Sponsored by the Meyer Fund
A Stacky Murphy’s Law for the Stack of Curves