We define and study the notion of hyper-Kahler category. On theoretical side, we focus on construction techniques deformation theory such categories. also in details some examples : non-commutative Hilbert schemes points a K3 surface categorical resolution relative compactified Prymian constructed by Markushevich Tikhomirov. *

Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of interest to ask to what extent K-theory remains \rigid" under this process. We show that some positive results can be obtained using ideas of Gabber, Gillet-...

In this paper we obtain the Cartier duality for k-schemes of commutative monoids functorially without providing the vector spaces of functions with a topology (as in [DGr, Exposé VIIB by P. Gabriel, 2.2.1]), generalizing a result for finite commutative algebraic groups by M. Demazure & P. Gabriel ([DG, II, §1, 2.10]). All functors we consider are functors defined over the category of commutativ...

Recall that a (hyper)graph is d-degenerate if every of its nonempty subgraphs has a vertex of degree at most d. Every d-degenerate (hyper)graph is (easily) (d + 1)colorable. A (hyper)graph is almost d-degenerate if it is not d-degenerate, but every its proper subgraph is d-degenerate. In particular, if G is almost (k − 1)-degenerate, then after deleting any edge it is k-colorable. For k ≥ 2, we...

A semigroup is a set of elements to which is related an operation usually called multiplication and an equivalence relation, such that the set is closed and associative relative to the operation. We shall discuss, briefly, finite semigroups which are uniquely factorable in the same sense as the multiplicative semigroup of all nonzero integers. Clifford' defined an arithmetic in such a way as to...

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...