7 papers
Cartier--Dieudonné Theory of Connected Group Schemes
Casimir Kothari, Joshua Mundinger
We prove that fiberwise-connected finite locally free commutative group schemes over a ring are equivalent to an explicit full subcategory of the derived category of modules ov…
Tannakian reconstruction in derived algebraic geometry
Joshua Mundinger, Shubhankar Sahai
We prove analogues of Tannakian reconstruction theorems of Lurie and Bhatt--Halpern-Leistner in \emph{derived} algebraic geometry, where the basic geometric objects are spectra of…
Cartier duality via Mittag-Leffler modules
Dima Arinkin, Joshua Mundinger
We construct the Cartier duality equivalence for affine commutative group schemes whose coordinate ring is a flat Mittag-Leffler module over an arbitrary base ring . The dua…
Poisson Manifolds of Compact Types with an Appendix by Joshua Mundinger
Marius Crainic, Rui Loja Fernandes, David Martínez Torres +1
We develop the theory of Poisson and Dirac manifolds of compact types, a broad generalization in Poisson and Dirac geometry of compact Lie algebras and Lie groups. We establish key…
On the differentials of the Hochschild-Kostant-Rosenberg spectral sequence
Joshua Mundinger
The Hochschild-Kostant-Rosenberg theorem implies the existence of a spectral sequence computing the Hochschild homology of a variety in terms of the cohomology of differential form…
Dieudonné theory for -smooth group schemes
Casimir Kothari, Joshua Mundinger
For all , there is a notion of an -smooth group scheme over any -algebra , which may be thought of as a ``Frobenius analogue" of an -truncated Bars…
Twisting the Infinitesimal Site
Joshua Mundinger
We classify twistings of Grothendieck's differential operators on a smooth variety in prime characteristic . We prove isomorphism classes of twistings are in bijection with…