One says that a variety X over Q violates the Hasse prin iple if X(Q v ) 6= ; for all ompletions Q v of Q (i.e., R and Q p for all primes p) but X(Q) = ;. Hasse proved that degree 2 hypersurfa es in P n satisfy the Hasse prin iple. In parti ular, if X is a genus 0 urve, then X satis es the Hasse prin iple, sin e the anti anoni al embedding of X is a oni in P 2 . Around 1940, Lind [Lin℄ and (ind...

The Hasse-Weil bound is a deep result in mathematics and has found wide applications in mathematics, theoretical computer science, information theory etc. In general, the bound is tight and cannot be improved. However, for some special families of curves the bound could be improved substantially. In this paper, we focus on the Hasse-Weil bound for the curve defined by y − y = f(x) over the fini...

Let $A$ be an abelian variety defined over a number field $k$, let $p$ odd prime and $F/k$ cyclic extension of $p$-power degree. Under not-too-stringent hypotheses we give interpretation the $p$-component relevant case equivariant Tamagawa conjecture in terms integral congruence relations involving evaluation on appropriate points ${\rm Gal}(F/k)$-valued height pairing Mazur Tate. We then discu...

We exhibit for each global field k an algebraic curve over k which violates the Hasse Principle. We can find such examples among Atkin-Lehner twists of certain elliptic modular curves and Drinfeld modular curves. Our main tool is a refinement of the “Twist Anti-Hasse Principle” (TAHP). We then use TAHP to construct further Hasse Principle violations, e.g. among curves over any number field of a...

In [18] Lorenz and Juhás raised the question of whether there exists a suitable formalism for the representation of infinite families of partial orders generated by Petri nets. Restricting ourselves to bounded p/t-nets, we propose Hasse diagram generators as an answer. We show that Hasse diagram generators are expressive enough to represent the partial order language of any bounded p/t net. We ...

1. The Hasse Principle(s) For Quadratic Forms Over Global Fields 1 1.1. Reminders on global fields 1 1.2. Statement of the Hasse Principles 2 2. The Hasse Principle Over Q 3 2.1. Preliminary Results: Reciprocity and Approximation 3 2.2. n ≤ 1 6 2.3. n = 2 6 2.4. n = 3 6 2.5. n = 4 8 2.6. n ≥ 5 9 3. The Hasse Principle Over a Global Field 9 3.1. n = 2 10 3.2. n = 3 10 3.3. n = 4 11 3.4. n ≥ 5 12...

If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs have the same length.

If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs have the same length.

Universally decodable matrices can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers L and n and a prime power q. Based on Pascal’s triangle we give an explicit construction of universally decodable matrices for any non-zero integers L and n and any prime power q where L ≤ q + 1. This is the largest set of possible par...