Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.

This paper presents a high speed and area efficient DWT processor VLSI based design for Image Compression applications. In this proposed design, pipelined partially serial architecture has been used to enhance the speed along with optimal utilization and resources available on the target FPGA. The architecture consists of two row processors, two column processors, and two memory modules. Each p...

Let T be a Noetherian ring and f a nonzerodivisor on T . We study concrete necessary and sufficient conditions for a module over R = T/(f) to be weakly liftable to T , in the sense of Auslander, Ding and Solberg. We focus on cyclic modules and get various positive and negative results on the lifting and weak lifting problems. For a module over T we define the loci for certain properties: liftab...

The classification of finite-dimensional pointed Hopf algebras with group S3 was finished in [AHS]: there are exactly two of them, the bosonization of a Nichols algebra of dimension 12 and a non-trivial lifting. Here we determine all simple modules over any of these Hopf algebras. We also find the Gabriel quivers, the projective covers of the simple modules, and prove that they are not of finit...

We prove a modularity lifting theorem for minimally ramified deformations of two-dimensional odd Galois representations, over an arbitrary number field. The main ingredient is a generalization of the Taylor-Wiles method in which we patch complexes rather than modules.

Winkler (1988) and Pauer (1992) present algorithms for a Hensel lifting of a modular Gröbner basis over lucky primes to a rational one. They have to solve a linear system with modular polynomial entries that requires another (modular) Gröbner basis computation. After an extension of luckiness to arbitrary (commutative noetherian) base rings we show in this paper that for a homogeneous polynomia...

This paper presents a DSP implementation of real-time JPEG 2000 encoder system. Among several modules in JPEG 2000 encoder, the lifting algorithm for discrete wavelet transform (DWT) and the embedded block coding with optimized truncation (EBCOT) comprise more than 85% of the encoding complexity. Thus, it is very important to design and optimize these two modules in order to increase the encodi...

The endoscopic transfer factor is expressed as difference of characters for the even and odd parts spin modules, or Dirac index trivial representation. lifting tempered in terms cohomology calculated explicitly.