Representability of Derived Bornological Stacks

Rhiannon Savage (University of Oxford)

Tuesday 19th November 15:00-16:00 Maths 311B

Abstract

Derived algebraic geometry can be considered as homotopical geometry relative
to the category of simplicial commutative rings. Similarly, new foundations for derived analytic and smooth geometry were proposed earlier this year by Ben-Bassat, Kelly, and Kremnizer as geometries relative to the category of simplicial commutative complete bornological
rings. In this talk I will introduce this framework and discuss a version of the Artin-Lurie
representability theorem which holds for derived stacks in these contexts. I will also briefly
discuss ongoing work showing representability of moduli stacks of Galois representations
and moduli stacks of solutions to PDEs. No knowledge of analytic or smooth geometry is
assumed.

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