cartier operator | Codes and the Cartier operator cartier operator We prove that a Cartier code is always a subcode of such a subfield subcode and prove Theorem 5.1 yielding an upper bound for the dimension of the corresponding quotient .
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0 · What makes the Cartier operator "tick"?
1 · Powers of the Cartier operator on Artin–Schreier covers
2 · POWERS OF THE CARTIER OPERATOR ON ARTIN
3 · Hasse–Witt matrix
4 · Di erential Forms in Positive Characteristic and the Cartier
5 · Codes and the Cartier operator
6 · Cartier operators on fields of positive characteristic
7 · Cartier operator in nLab
8 · Application of the Cartier operator in coding theory
9 · APPLICATION OF THE CARTIER OPERATOR IN CODING
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map and the Cartier isomorphism yields a map C : H0(X; 1 X) !H 0(X(p); 1 (p)) which is called the Cartier operator (note: this map need not be an isomorphism). Page 3 of6 Cartier operator in nLab. Contents. Notation. The Cartier Isomorphism. Relation to the Hodge-de Rham Spectral Sequence. The Generalization to Non-commutative algebra. .
For $A$ regular, the Cartier operator $\cC: H^{\bullet} \to \Omega^{\bullet}$ is the inverse to $\cF$. In particular, if $A$ regular of dimension $, then we can take the composition .ier operators is of an algebraic and arithmetic nature. In this paper, from a purely analytical perspective, we consider two types of Cartier op-erators (or maps) which act on a non .
We use the Cartier operator on H 0 (A 2, Ω 1) to find a closed formula for the a-number of the form A 2 = v (Y q + Y − x q + 1 2) where q = p s over the finite field F q 2. The . We prove that a Cartier code is always a subcode of such a subfield subcode and prove Theorem 5.1 yielding an upper bound for the dimension of the corresponding quotient .POWERS OF THE CARTIER OPERATOR ON ARTIN-SCHREIER COVERS. ABSTRACT. Curves in positive characteristic have a Cartier operator acting on their space of regular .APPLICATION OF THE CARTIER OPERATOR IN CODING THEORY VAHID NOUROZI Abstract. The a-number is an invariant of the isomorphism class of the p-torsion group .
In this paper, I generalize that approach to arbitrary powers of the Cartier operator, yielding bounds for the dimension of the kernel. These bounds give new restrictions on the Ekedahl .
Download a PDF of the paper titled Application of the Cartier Operator in Coding Theory, by Vahid Nourozi
HASSE–WITT AND CARTIER–MANIN MATRICES 5 1.3. Adjointness. Let V be the dual vector space of V and let (;): V V !Kbe the natural pairing. Continue to let f: V !V be -linear, and letFor a curve in positive characteristic, the Cartier operator acts on the vector space of its regular differentials. The a-number is defined to be the dimension of the kernel of the Cartier . The a-number is an invariant of the isomorphism class of the p-torsion group scheme.We use the Cartier operator on H 0 ( A 2, Ω 1 ) to find a closed formula for the a . The a-number is an invariant of the isomorphism class of the p-torsion group scheme. We use the Cartier operator on H 0 (A 2 , Ω 1) to find a closed formula for the a .
the action of the Cartier operator on H0(A 2,Ω1). 2. The Cartier operator Let k be an algebraically closed field of characteristic p > 0. Let C be a curve defined over k. The Cartier operator is a .together with some basic features of the Cartier operator, we prove a vanishing property of this map in Section 3. In Section 4, we introduce Cartier codes. We compare them with subfield .codes and the Cartier operator, we improve in Corollary 6.5 the known estimates for the dimension of subfield subcodes of AG codesCΩ(D,G)|F q whenG is non-positive. .the action of the Cartier operator operator on H0(C,Ω1 C). Finally, Section 4 contain the proof of Theorem 1.1 and Corollary 1.3 The author would like to thank Dr. Rachel Pries for her .
A few results on the rank of the Cartier operator (especially a-number) of curves are introduced by Kodama and Washio [9], González [4], Pries and Weir [12], Yui [24] and . Cartier operator In [3], Cartier defines an operator C on the sheaf 1 C satisfying the following properties: ) C (ω 1 +ω 2 )=C (ω 1 )+C (ω 2 ), ) C (h p ω)= hC (ω), ) C (dz)= 0, . The ring of Frobenius operators. A dual concept to that of a Cartier map (or Cartier operator) is that of a Frobenius operator. Let (R, m) be a local commutative ring of positive .
codes and the Cartier operator, we improve in Corollary 6.5 the known estimates for the dimension of subfield subcodes of AG codesCΩ(D,G)|F q whenG is non-positive. . [Show full abstract] Cartier operator, yielding bounds for the dimension of the kernel. These bounds give new restrictions on the Ekedahl-Oort type of Artin-Schreier covers.map and the Cartier isomorphism yields a map C : H0(X; 1 X) !H 0(X(p); 1 (p)) which is called the Cartier operator (note: this map need not be an isomorphism). Page 3 of6
This is now called the Cartier–Manin operator (sometimes just Cartier operator), for Pierre Cartier and Yuri Manin. The connection with the Hasse–Witt definition is by means of Serre duality, . Cartier operator in nLab. Contents. Notation. The Cartier Isomorphism. Relation to the Hodge-de Rham Spectral Sequence. The Generalization to Non-commutative algebra. .
What makes the Cartier operator "tick"?
Powers of the Cartier operator on Artin–Schreier covers
For $A$ regular, the Cartier operator $\cC: H^{\bullet} \to \Omega^{\bullet}$ is the inverse to $\cF$. In particular, if $A$ regular of dimension $, then we can take the composition .
ier operators is of an algebraic and arithmetic nature. In this paper, from a purely analytical perspective, we consider two types of Cartier op-erators (or maps) which act on a non . We use the Cartier operator on H 0 (A 2, Ω 1) to find a closed formula for the a-number of the form A 2 = v (Y q + Y − x q + 1 2) where q = p s over the finite field F q 2. The .
POWERS OF THE CARTIER OPERATOR ON ARTIN
We prove that a Cartier code is always a subcode of such a subfield subcode and prove Theorem 5.1 yielding an upper bound for the dimension of the corresponding quotient .
Hasse–Witt matrix
POWERS OF THE CARTIER OPERATOR ON ARTIN-SCHREIER COVERS. ABSTRACT. Curves in positive characteristic have a Cartier operator acting on their space of regular .APPLICATION OF THE CARTIER OPERATOR IN CODING THEORY VAHID NOUROZI Abstract. The a-number is an invariant of the isomorphism class of the p-torsion group .
Di erential Forms in Positive Characteristic and the Cartier
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cartier operator|Codes and the Cartier operator
