WebFeb 13, 2014 · Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time David Harvey, Andrew V. Sutherland We present an efficient algorithm … In mathematics, the Hasse–Witt matrix H of a non-singular algebraic curve C over a finite field F is the matrix of the Frobenius mapping (p-th power mapping where F has q elements, q a power of the prime number p) with respect to a basis for the differentials of the first kind. It is a g × g matrix … See more This definition, as given in the introduction, is natural in classical terms, and is due to Helmut Hasse and Ernst Witt (1936). It provides a solution to the question of the p-rank of the Jacobian variety J of C; the p-rank is bounded by … See more The p-rank of an abelian variety A over a field K of characteristic p is the integer k for which the kernel A[p] of multiplication by p has p points. It may … See more The interpretation for sheaf cohomology is this: the p-power map acts on H (C,OC), or in other words the first cohomology of C with coefficients in its structure sheaf. This is now called the Cartier–Manin operator (sometimes just … See more The case of elliptic curves was worked out by Hasse in 1934. Since the genus is 1, the only possibilities for the matrix H are: H is zero, Hasse invariant 0, p-rank 0, the supersingular case; or H non-zero, Hasse invariant 1, p-rank 1, the ordinary case. Here there is a … See more
Hasse–Witt matrix - Wikipedia
WebIn mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br ( K ). The name "Hasse–Witt" comes from … WebComputing Hasse{Witt matrices of hyperelliptic curves in average polynomial time David Harvey and Andrew V. Sutherland Abstract We present an e cient algorithm to compute … ffxiv buried memory release date
BSTRACT 1 X arXiv:1710.10726v5 [math.NT] 7 Feb 2024
WebThe matrix W p depends on the equation y2 = f(x) mod pfor the curve C p, but its conjugacy class, and in particular, its characteristic polynomial, is an invariant of the function eld of C p. The Hasse{Witt matrix W pis closely related to the zeta function (1) Z p(T) := exp X1 k=1 #C p(F pk) k Tk! = L p(T) (1 T)(1 pT): Indeed, the numerator L ... WebMargaret Hasse (born 1950, in South Dakota), is a poet and writer who has lived and worked in Minnesota since graduating from Stanford University in 1973. Three of her … WebVia Serre duality, one can formally relate the Hasse-Witt matrix, which is defined in terms of the p -power Frobenius acting on H 1 ( C, O C), where O C is the structure sheaf, with … ffxiv burden of the father savage