A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, −KX , is an ample Cartier divisor. The importance of Fano varieties is twofold, from one side they give, has predicted by Fano [Fa], examples of non rational varieties having plurigenera and irregularity all zero (cfr [Is]); on the other hand they should be the building block of uniruled variety, indee...

Let O denote the ring of integers in a p-adic local field. Recall that O-modules are formal groups with an O-action such that the induced action on the Lie algebra is via scalars. In the paper this notion is generalised to finite flat group schemes. It is shown that the usual properties carry over. For example, Cartier duality holds with the multiplicative group replaced by the Lubin–Tate group...

In [Pas15], we described the Minimal Model Program in the family of Q-Gorenstein projective horospherical varieties, by studying a family of polytopes defined from the moment polytope of an ample Q-Cartier Q-divisor of the variety we begin with. Here, we summarize the results of [Pas15] and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs (X,∆) wher...

We prove a theorem on algebraic osculation and we apply our result to the Computer Algebra problem of polynomial factorization. We consider X a smooth completion of C and D an effective divisor with support ∂X = X \ C. Our main result gives explicit conditions equivalent to that a given Cartier divisor on the subscheme (|D|,OD) extends to X. These osculation criterions are expressed with residu...

Abstract This paper is a continuation of our Dwork crystals series. Here we exploit the Cartier operation to prove supercongruences for expansion coefficients rational functions. In process, it appears that excellent Frobenius lifts are driving force behind supercongruences. Originally introduced by Dwork, these have occurred rather infrequently in literature, and only context families elliptic...

Abstract The finite dual $H^{\circ}$ of an affine commutative-by-finite Hopf algebra H is studied. Such a extension commutative A by dimensional $\overline{H}$ . main theorem gives natural conditions under which decomposes as crossed or smash product $\overline{H}^{\ast}$ the $A^{\circ}$ This decomposition then further analysed using Cartier–Gabriel–Kostant to obtain component subalgebras mappi...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

We prove that the F -jumping numbers of the test ideal τ(X ; ∆, a) are discrete and rational under the assumptions that X is a normal and F -finite variety over a field of positive characteristic p, KX + ∆ is Q-Cartier of index not divisible p, and either X is essentially of finite type over a field or the sheaf of ideals a is locally principal. This is the largest generality for which discrete...