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de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities

Matthew Satriano — 2012

Annales de l’institut Fourier

We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic p (as defined by Abramovich, Olsson, and Vistoli) which lift mod p 2 degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.

On a notion of “Galois closure” for extensions of rings

Manjul Bhargava;  Matthew Satriano — 2014

Journal of the European Mathematical Society

We introduce a notion of “Galois closure” for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an S n degree n extension of fields. Moreover, we prove a number of properties of this construction; for example, we show that it is functorial and respects base change. We also investigate the behavior of this Galois closure construction for various natural classes of ring extensions.

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