Arithmetic in generalized Artin-Schreier extensions of k(x)

Madden, Daniel J.

doi:10.1016/0022-314x(78)90027-6

Cited by 21 publications

(45 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As explained in the proof of Lemma , we cannot have partial ramification and equal ramification indices. Secondly, a generalised Artin–Schreier extension is a cyclic extension of degree equal to a power of the characteristic of k , and it was proven by Madden that such an extension may be expressed as a tower of Artin–Schreier extensions

A_{i} = A_{i, m_{i}} / A_{i, m_{i} - 1} / \dots / A_{i, 1} = K

with, for each

j = 1, \dots, m_{i}

, some generator

y_{i, j}

A_{i, j} / A_{i, j - 1}

possessing defining equation

y_{i, j}^{p} - y_{i, j} = c_{i, j}

in global standard form. The following structure of

L / K

is natural for immediately arriving at global standard form in a tower from the composites of cyclic extensions over K .…”

Section: Standard Formmentioning

confidence: 99%

“…Boseck's basis has known generalisations to other settings. For example, for elementary abelian extensions, Garcia used bases of this type for elementary abelian extensions to compute Weierstrass points, and Madden used these to calculate the rank of the Hasse–Witt matrix. Boseck bases may also be used to understand the

k [G]

‐module structure of the k ‐vector space

Ω_{L}

of holomorphic differentials of the field L .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Holomorphic differentials of certain solvable covers of the projective line over a perfect field

Marques

Ward

2018

Mathematische Nachrichten

View full text Add to dashboard Cite

show abstract

A_{i} = A_{i, m_{i}} / A_{i, m_{i} - 1} / \dots / A_{i, 1} = K

with, for each

j = 1, \dots, m_{i}

, some generator

y_{i, j}

A_{i, j} / A_{i, j - 1}

possessing defining equation

y_{i, j}^{p} - y_{i, j} = c_{i, j}

in global standard form. The following structure of

L / K

is natural for immediately arriving at global standard form in a tower from the composites of cyclic extensions over K .…”

Section: Standard Formmentioning

confidence: 99%

k [G]

‐module structure of the k ‐vector space

Ω_{L}

of holomorphic differentials of the field L .…”

Section: Introductionmentioning

confidence: 99%

Holomorphic differentials of certain solvable covers of the projective line over a perfect field

Marques

Ward

2018

Mathematische Nachrichten

View full text Add to dashboard Cite

show abstract

“…D. J. Madden [6] has shown that each /ί/^ί-ι has a generation of the form described in Lemma l . Let P be the restriction of P to P).…”

Section: Lemma 1 Let F/k Be An Algebraic Function Field Lei E/f Be mentioning

confidence: 99%

Subfields of cyclic p-extensions of K(x).

1981

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

“…Now, if the third entry of a triple (8) of the space (7) vanishes, then f 0 and f ∞ glue to a global and hence constant function and the whole triple vanishes. Hence, the triples in (26) and (27) are equal already before taking residue classes.…”

Section: Proof Of Theorem 43mentioning

confidence: 99%

“…We use the notationsȞ 1 dR (U ) andȞ 1 dR (U ) for the representations of H 1 dR (X/k) introduced in (7), (8) and (16), (17), respectively. The canonical isomorphism ρ :Ȟ 1 dR (U ) → H 1 dR (U ), is then induced by the projection…”

Section: Theorem 32 If P = 2 the Residue Classesmentioning

confidence: 99%

On the de-Rham cohomology of hyperelliptic curves

Köck

Tait

2018

Res. number theory

View full text Add to dashboard Cite

For any hyperelliptic curve X , we give an explicit basis of the first de-Rham cohomology of X in terms ofČech cohomology. We use this to produce a family of curves in characteristic p > 2 for which the Hodge-de-Rham short exact sequence does not split equivariantly; this generalises a result of Hortsch. Further, we use our basis to show that the hyperelliptic involution acts on the first de-Rham cohomology by multiplication by −1, i.e., acts as the identity when p = 2.

show abstract

Arithmetic in generalized Artin-Schreier extensions of k(x)

Cited by 21 publications

References 6 publications

Holomorphic differentials of certain solvable covers of the projective line over a perfect field

Holomorphic differentials of certain solvable covers of the projective line over a perfect field

Subfields of cyclic p-extensions of K(x).

On the de-Rham cohomology of hyperelliptic curves

Contact Info

Product

Resources

About