Choices of HKR isomorphisms

2023/10/09 by Robalo, Marco · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2310.05859

Abstract

In this short note we record the fact that the set of multiplicative HKR natural equivalences defined simultaneously for all derived schemes, functorialy splitting the HKR-filtration and rendering the circle action compatible with the de Rham differential, is, via Cartier duality, in a natural bijection with the set of filtered formal exponential maps \widehat\mathbbG_a→ \widehat\mathbbG_m. In particular, when the base k is a field of characteristic zero, the set of choices is k^∗.

Cited by

• Hochschild-Kostant-Rosenberg isomorphism for derived Deligne-Mumford stacks

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• Functoriality of HKR isomorphisms
• Formality of derived intersections and the orbifold HKR isomorphism
• S¹-Equivariant simplicial algebras and de Rham theory
• Cartier isomorphism and Hodge Theory in the non-commutative case
• Filtered formal groups, Cartier duality, and derived algebraic geometry