When a finite group G acts faithfully on a graded integral domain S which is an algebra over a field k, such as a polynomial ring, we consider S as a kG-module. We show that S is asymptotically mostly projective in each degree, and also that it is in fact mostly free in an appropriate sense. Similar results also hold for filtered algebras, such as power series rings.

Abstract We develop filtered-graded techniques for algebras in monoidal categories with the main goal of establishing a categorical version Bongale’s 1967 result: filtered deformation Frobenius algebra over field is as well. Toward goal, we first construct associated graded functor, building on prior works Ardizzoni and Menini, Galatius et al., Gwillian Pavlov. Next, produce equivalent conditio...

Let k be a finite field of characteristic p>0, W(k) the ring Witt vectors k, X smooth scheme over specW(k) dimension <p-1 and 0 special fiber X. In 1987, Deligne Illusie proved degeneration spectral sequence “de Hodge vers de Rham” in purely algebraic way, by constructing quasi-isomorphism at level derived categories between Rham complex with differentials. Simultaneously Fontaine Messing const...

Correct modelling of solar photovoltaic (PV) system yields is necessary to optimize system design, improve reliability of projected outputs to ensure favourable project financing and to facilitate proper operations and maintenance. An improved methodology for fine resolution modelling of PV systems is presented using module short-circuit current (Isc) at 5-minute time-scales, and clearly identi...

Correct modelling of solar photovoltaic (PV) system yields is necessary to optimize system design, improve reliability of projected outputs to ensure favourable project financing and to facilitate proper operations and maintenance. An improved methodology for fine resolution modelling of PV systems is presented using module short-circuit current (Isc) at 5-minute time-scales, and clearly identi...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.