We construct liftings of reduction maps from CM points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with a given conductor and CM points on certain corresponding totally definite quaternion algebras.

Abstract It is well known that classical varieties of $\Sigma$ -algebras correspond bijectively to finitary monads on $\mathsf{Set}$ . We present an analogous result for ordered -algebras, is, categories algebras presented by inequations between -terms. prove they strongly $\mathsf{Pos}$ That those which preserve reflexive coinserters. deduce have a coinserter presentation, the coequalizer pres...

Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.

The Hochschild cohomology of a tensor product algebras is isomorphic to graded algebras, as Gerstenhaber algebra. A similar result holds when the twisted by bicharacter. We present new proofs these isomorphisms, using Volkov’s homotopy liftings that were introduced for handling brackets expressed on arbitrary bimodule resolutions. Our results illustrate utility theoretical purposes.

A major part of this paper is devoted to an in-depth study j -operators and their properties. This enables us obtain several results on liftings weak DG modules along simple extensions algebras unify the proofs existing obtained by authors these subjects. Finally, we provide a new characterization (weak) lifting property algebras.

For an arbitrary rational polyhedron we consider its decompositions into Minkowski summands and, dual to this, the free extensions of associated pair semigroups. Being for semigroups is equivalent flatness corresponding algebras. Our main result phrased in this setup: category always contains initial object, which describe explicitly. These objects seem be related unique liftings log geometry. ...