Abstract Given a continuous, odd, reducible, and semi-simple $2$-dimensional representation $\bar \rho _{0}$ of $G_{{\mathbb{Q}},Np}$ over finite field odd characteristic $p$, we study the relation between universal deformation ring pseudo-representation corresponding to (pseudo-deformation ring) big $p$-adic Hecke algebra prove that maximal reduced quotient pseudo-deformation is isomorphic loc...

A conjecture on vanishing and non-negativity of intersection multiplicity on the blow-up of a regular local ring at its closed point has been proposed. Proofs of vanishing, several special cases of non-negativity and a sufficient condition for non-negativity of this conjecture are described. The topic on intersection multiplicity on vector bundles is also addressed. Introduction. Let X be a reg...

In the title mol-ecular salt, C(11)H(17)N(2) (+)·Cl(-), the piperazin-1-ium ring adopts a chair conformation with the aromatic ring in a pseudo-equatorial orientation. The dihedral angle between the benzene ring and the mean plane of the piperazin-1-ium ring is 51.22 (6)°. In the crystal, N-H⋯Cl hydrogen bonds link the mol-ecules into chains propagating in [100]. Weak C-H⋯π inter-actions also o...

Denef and Loeser defined a map from the Grothendieck ring of sets definable in pseudo-finite fields to the Grothendieck ring of Chow motives, thus enabling to apply any cohomological invariant to these sets. We generalize this to perfect, pseudo algebraically closed fields with pro-cyclic Galois group. In addition, we define some maps between different Grothendieck rings of definable sets which...