Hasse witt matrix
WebHASSE–WITT AND CARTIER–MANIN MATRICES: A WARNING AND A REQUEST JEFFREY D. ACHTER AND EVERETT W. HOWE ABSTRACT.Let X be a curve in positive characteristic. A Hasse–Witt matrix for X is a matrix that represents the action of the Frobenius operator on the cohomology group H1(X,O X) with respect to 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 …
Hasse witt matrix
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WebJan 1, 2024 · This matrix is closely related to the Hasse-Witt matrix B of X, which is defined as the matrix of the p-power Frobenius operator acting on H 1 (X, O X ) with respect to some basis. WebFeb 13, 2014 · Our method employs the Hasse-Weil bounds in conjunction with the Hasse-Witt matrix for superelliptic curves, whose entries we express in terms of multinomial coefficients. We present a fast ...
WebHere is a useful repository of articles on Witt vectors. (The functor of p-typical Witt vectors provides the right adjoint to the forgetful functor from delta rings to rings.) ... 10 and 11; note that the proof of the connection between the Cartier operator on holomorphic differentials and the Hasse--Witt matrix that I give in my notes is ... 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
Webthe Hasse-Witt-matrix is proved, if the degree divides p — 1. The same theorem for the generic hypersurface follows then from the semicontinuity of the matrix rank. The § 3 is … 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 …
WebFeb 13, 2014 · Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time David Harvey, Andrew V. Sutherland We present an efficient algorithm …
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 ... dsw earth origins belle brielleWebrecurrence relations used to derive the Hasse{Witt matrix in [1], whose coe cients do depend on p, and which are analogous to the ‘horizontal reductions’ in [10] and [12]. Second, we only need to know the coe cients of each vector v n modulo p= 2n+ 1. The essential di culty here is that the modulus is di erent for each n. Following [12], we use commissary rock island ilWebHASSE INVARIANTS FOR HILBERT MODULAR VARIETIES EYAL Z. GOREN Abstract. Given a totally real eld Lof degree g, we construct g Hasse invariants on Hilbert modular varieties in characteristic pand characterize their divisors. We show that these divisors give the type strati cation de ned by the action of O Lon the p-elementary subgroup. commissary roy choiWebhyperelliptic curve defined by y2 = x 2g+l - x has a zero Hasse-Witt matrix if and only if p = -1 or 2g+ 1 (rood 4g). The hyperelliptic curve defined _b_g y2= x2g+l 1 has a zero Hasse-Witt matrix if and only if p= -1 (mod2g+l). Proof. We provide a proof of the first statement. The proof of the second ds wealth limitedWebSep 1, 2024 · When the Hasse–Witt matrix is invertible, there exists a unit root part of the F-crystal. We consider the p-adic approximation of the Frobenius matrix on the unit root … dsw earth origins sandalsWebMargaret 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 … commissary salaryWebMar 5, 2012 · The local Hasse invariants determine the class of $A$ uniquely. They are related by the following conditions: 1) there are only finitely-many valuations $\nu$ for … ds wear