Summary: ADEQUATE MODULI SPACES AND
GEOMETRICALLY REDUCTIVE GROUP SCHEMES
JAROD ALPER
Abstract. We develop the theory of adequate moduli spaces in characteristic p (and mixed
characteristic) characterizing quotients by geometrically reductive group schemes.
Contents
1. Introduction 1
2. Conventions 4
3. Adequacy 5
4. Adequately affine morphisms 11
5. Adequate moduli spaces 16
6. Finiteness results 22
7. Uniqueness of adequate moduli spaces 25
8. Coarse moduli spaces 27
9. Geometrically reductive group schemes and GIT 29
References 38
1. Introduction
Motivation. In characteristic 0, any representation of a finite group G is completely reducible.
Therefore, the functor from G-representations to vector spaces V V G
given by taking invariants

Source: Alper, Jarod - Department of Mathematics, Columbia University

Collections: Mathematics