We construct a locally geometric ∞-stack MHod(X,Perf) of perfect complexes with λ-connection structure on a smooth projective variety X. This maps to A1/Gm, so it can be considered as the Hodge filtration of its fiber over 1 which is MDR(X,Perf), parametrizing complexes of DX-modules which are OX -perfect. We apply the result of Toen-Vaquié that Perf(X) is locally geometric. The proof of geomet...

The purpose of this note is to provide for my algebra class a guide to the proof of Cohen's structure theorem for complete local rings as given by Cohen himself, in the original 1946 paper [C]. In spite of more modern and concise treatments by the likes of Nagata and Grothendieck, the original proof is a model of clarity and the entire paper is a commutative algebra masterpiece. First, a few wo...

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néro...

for any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. the condition is that every minimal ideal of the ring consist entirely of bounded elements. it is not too stringent, and is satisfied, for instance, by rings of conti...

For cryptographic applications, the behaviour of the difference map is of importance and since there are no perfect nonlinear (PN) permutations, almost perfect nonlinear (APN) permutations have attracted a lot of attention in the last decades. Costas permutations, which are also extreme with respect to the behaviour of their difference maps, were originally introduced in connection with applica...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...

In this paper, we develop the theory of Jacobian rings of open complete intersections, which mean a pair (X,Z) where X is a smooth complete intersection in the projective space and and Z is a simple normal crossing divisor in X whose irreducible components are smooth hypersurface sections on X . Our Jacobian rings give an algebraic description of the cohomology of the open complement X − Z and ...

An (s; n; q; t)-perfect hash family is a set of functions 1 ; 2 ; : : :; s from a set V of cardinality n to a set F of cardinality q with the property that every t-subset of V is injectively mapped into F by at least one of the functions i. The paper shows that the maximum value n s;t (q) that n can take for xed s and t has a leading term that is linear in q if and only if t > s. Moreover, for ...

The transfer of multiple protons in hydrogen-bonded networks usually occurs one proton at a time. At sufficiently high temperatures, each proton transfers via thermally activated hopping along its hydrogen bond, thereby moving a charge defect through the network. At low temperatures, quantum-mechanical tunnelling might set in instead, thus avoiding hopping over the energy barriers. In the case ...

Certain subgraphs of a given graph G restrict the minimum number χ(G) of colors that can be assigned to the vertices of G such that the endpoints of all edges receive distinct colors. Some of such subgraphs are related to the celebrated Strong Perfect Graph Theorem, as it implies that every graph G contains a clique of size χ(G), or an odd hole or an odd anti-hole as an induced subgraph. In thi...