Lifting of the additive group scheme actions

Group actions on curves and the lifting problem

1.1 The lifting problem The problem we are concerned with in our lectures and which we shall refer to as the lifting problem was originally formulated by Frans Oort in [17]. To state it, we fix an algebraically closed field κ of positive characteristic p. Let W (κ) be the ring of Witt vectors over κ. Throughout our notes, o will denote a finite local ring extension of W (κ) and k = Frac(o) the ...

Separating Invariants for Arbitrary Linear Actions of the Additive Group

We consider an arbitrary representation of the additive group Ga over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.

Motivic Homotopy Theory of Group Scheme Actions

We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic K-theory is representable in the resulting homotopy category. Additionally, we establish homotopical purity and blow-up theorems for finite abelian groups.

Wavelets and the Lifting Scheme

Lifting Scheme of Wavelet Transform

The Wim Sweldens developed the lifting scheme for the construction of biorthogonal wavelets. The main feature of the lifting scheme is that all constructions are derived in the spatial domain. It does not require complex mathematical calculations that are required in traditional methods. Lifting scheme is simplest and efficient algorithm to calculate wavelet transforms. It does not depend on Fo...