TY - JOUR

T1 - Bicyclic algebras of prime exponent over function fields

AU - Kunyavskiǐ, Boris È

AU - Rowen, Louis H.

AU - Tikhonov, Sergey V.

AU - Yanchevskiǐ, Vyacheslav I.

PY - 2006/6

Y1 - 2006/6

N2 - We examine some properties of bicyclic algebras, i.e. the tensor product of two cyclic algebras, defined over a purely transcendental function field in one variable. We focus on the following problem: When does the set of local invariants of such an algebra coincide with the set of local invariants of some cyclic algebra? Although we show this is not always the case, we determine when it happens for the case where all degeneration points are defined over the ground field. Our main tool is Faddeev's theory. We also study a geometric counterpart of this problem (pencils of Severi-Brauer varieties with prescribed degeneration data).

AB - We examine some properties of bicyclic algebras, i.e. the tensor product of two cyclic algebras, defined over a purely transcendental function field in one variable. We focus on the following problem: When does the set of local invariants of such an algebra coincide with the set of local invariants of some cyclic algebra? Although we show this is not always the case, we determine when it happens for the case where all degeneration points are defined over the ground field. Our main tool is Faddeev's theory. We also study a geometric counterpart of this problem (pencils of Severi-Brauer varieties with prescribed degeneration data).

UR - http://www.scopus.com/inward/record.url?scp=33744789993&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-05-03772-4

DO - 10.1090/S0002-9947-05-03772-4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:33744789993

SN - 0002-9947

VL - 358

SP - 2579

EP - 2610

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 6

ER -