Pluri-Canonical Models of Supersymmetric Curves

This paper is about pluri-canonical models of supersymmetric (susy) curves. Susy curves are generalisations of Riemann surfaces in the realm of super geometry. Their moduli space is a key object in supersymmetric string theory. We study the pluri-canonical models of a susy curve, and we make some considerations about Hilbert schemes and moduli spaces of susy curves.Comment: To appear in the proceedings of the intensive period "Perspectives in Lie Algebras", held at the CRM Ennio De Giorgi, Pisa, Italy, 201

Direct twisted Galois stratification

The theory ACFA admits a primitive recursive quantifier elimination procedure. It is therefore primitive recursively decidable

Tannakian properties of unit Frobenius-modules

We show that unit $\mathcal{O}_{F,X}^\Lambda$-modules of Emerton and Kisin provide an analogue of locally constant sheaves in the context of B\"ockle-Pink $\Lambda$-crystals. For example they form a tannakian category if the coefficient algebra $\Lambda$ is a field. Our results hold for a big class of coefficien algebras which includes Drinfeld rings, and for arbitary locally noetherian base schemes.Comment: 10 pages; lemma 2.3 replaced with a reference to Bourbaki; some misprints correcte