Let K be a finite extension of
, and E be an elliptic curve over K with good ordinary reduction. We study the cyclic length of the p-primary part of the Brauer group of E. In particular, for
, we ...show that all elements in the p-torsion of
are p-cyclic whenever p divides the number of
-points of the reduction of E modulo p.
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3.
Linkage of sets of cyclic algebras Chapman, Adam
Journal of pure and applied algebra,
March 2022, 2022-03-00, Volume:
226, Issue:
3
Journal Article
Peer reviewed
Open access
Let p be a prime integer and F the function field in two algebraically independent variables over a smaller field F0. We prove that if char(F0)=p⩾3 then there exist p2−1 cyclic algebras of degree p ...over F that have no maximal subfield in common, and if char(F0)=0 then there exist p2 cyclic algebras of degree p over F that have no maximal subfield in common.
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In this paper, we introduce the notion of perfect space-time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral ...efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas
In this note, we present a chain lemma for biquaternion algebras over fields of characteristic 2 in the style of the equivalent chain lemma by Sivatski in characteristic not 2, and conclude a bound ...on the symbol length of classes in
2
n
B
r
(
F
)
whose symbol length in
2
n
+
1
B
r
(
F
)
is at most 4.
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We obtain two results about the p-primary part of the Brauer group of a p-adic curve X. First, assuming enough roots of unity and that X has good reduction, we construct indecomposable K(X)-division ...algebras of period p
2
and index p
3
. Second, for an elliptic curve X with split multiplicative reduction, we show that all order p elements of
are
-cyclic, and that if moreover X is defined over
that all order p
r
elements of
are
-cyclic for
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We discuss the Kummer subspaces of tensor products of cyclic algebras, focusing mainly on the case of cyclic algebras of degree 3. We present a family of maximal Kummer spaces in any tensor product ...of cyclic algebras of prime degree, classify all the monomial Kummer spaces in tensor products of cyclic algebras of degree 3, and provide an upper bound for the dimension of Kummer spaces in the generic tensor product of cyclic algebras of degree 3.
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We prove that if two division p-algebras of prime degree share an
inseparable field extension of the center then they also share a
cyclic separable one. We show that the converse is in general not
...true. We also point out that sharing all the inseparable field
extensions of the center does not imply sharing all the cyclic
separable ones.
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The Picard group of Brauer-Severi varieties Badr, Eslam; Bars, Francesc; García, Elisa Lorenzo
Open mathematics (Warsaw, Poland),
10/2018, Volume:
16, Issue:
1
Journal Article
Peer reviewed
Open access
In this paper, we provide explicit generators for the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular,we provide such generators for all Brauer-Severi ...surfaces. To produce these generators we use the theory of twists of smooth plane curves.
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