Chilean number theorist
Ricardo Baeza Rodríguez is a Chilean mathematician who works as a professor at the University of Talca .[ 1] [ 2] Saarland University , under the joint supervision of Robert W. Berger and Manfred Knebusch.[ 2] [ 3] number theory .[ 4]
Career
Baeza became a member of the Chilean Academy of Sciences in 1983.[ 1] National Prize for Exact Sciences .[ 2] [ 4] fellows of the American Mathematical Society , the only Chilean to be so honored.[ 2] [ 5]
Research
In 1990, Baeza proved the norm theorem over characteristic two; it had been previously proved in other characteristics.[ 6] q is a nonsingular quadratic form over a field F , and
π
(
t
)
∈
F
[
t
]
{\displaystyle \pi (t)\in F[t]}
irreducible polynomial (with
F
(
π
)
:=
F
[
t
]
/
π
(
t
)
{\displaystyle F(\pi ):=F[t]/\pi (t)}
field extension ), then
(
π
(
t
)
)
⊗
q
≅
q
{\displaystyle (\pi (t))\otimes q\cong q}
q
⊗
F
(
π
)
{\displaystyle q\otimes F(\pi )}
[ 6]
In 1992, Baeza and Roberto Aravire introduced a modification of Milnor's k-theory for quadratic forms over a field of characteristic two.[ 7]
W
q
(
F
)
{\displaystyle W_{q}(F)}
Witt group of quadratic forms over a field F , then one can construct a group
k
n
(
F
)
{\displaystyle k_{n}(F)}
isomorphism
s
n
:
h
n
(
F
)
→
I
n
−
1
W
q
(
F
)
/
I
n
W
q
(
F
)
{\displaystyle s_{n}:h_{n}(F)\to I^{n-1}W_{q}(F)/I^{n}W_{q}(F)}
n .[ 7]
In 2003, Baeza and Aravire studied quadratic forms and differential forms over certain function fields of an algebraic variety of characteristic two.[ 8] Knebusch's degree conjecture .[ 8]
In 2007, Baeza and Arason found a group presentation of the groups
I
n
(
K
)
⊂
W
(
K
)
{\displaystyle I^{n}(K)\subset W(K)}
n -fold bilinear Pfister forms , and of the groups
I
n
W
q
(
K
)
⊂
W
q
(
K
)
{\displaystyle I^{n}W_{q}(K)\subset W_{q}(K)}
[ 9]
Publications
Baeza, Ricardo (2006). Quadratic Forms Over Semilocal Rings . Springer. ISBN 9783540358169
References
^ a b Member profile , Chilean Academy of Sciences, retrieved 2015-01-12.^ a b c d "Miembro de Excelencia: Ricardo Baeza será distinguido por la American Mathematical Society" , Sala de Prensa , University of Talca, November 16, 2012, retrieved 2015-01-12 ^ Ricardo Baeza Rodríguez at the Mathematics Genealogy Project .^ a b "Ricardo Baeza gana Premio Nacional de Ciencias Exactas" , Nacion.cl , August 27, 2009^ List of Fellows of the American Mathematical Society , retrieved 2015-01-12.^ a b Baeza, Ricardo (1990). "The norm theorem for quadratic forms over a field of characteristic 2" . Communications in Algebra . 18 (5): 1337– 1348. doi :10.1080/00927879008823968 . ISSN 0092-7872 . ^ a b Aravire, Ricardo; Aravire, Roberto (1992). "Milnor'ory and quadratic forms over fields of characteristic two" . Communications in Algebra . 20 (4): 1087– 1107. doi :10.1080/00927879208824393 . ISSN 0092-7872 . ^ a b Aravire, Roberto; Baeza, Ricardo (2003). "The behavior of quadratic and differential forms under function field extensions in characteristic two" . Journal of Algebra . 259 (2): 361– 414. doi :10.1016/S0021-8693(02)00568-9 . ^ Arason, Jón Kr.; Baeza, Ricardo (August 2007). "Relations in I n and I n W q in characteristic 2" . Journal of Algebra . 314 (2): 895– 911. doi :10.1016/j.jalgebra.2007.05.004 .
External links
![{\displaystyle \pi (t)\in F[t]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac4c15ace30a2f34c29ddfe66f14abc7b5b42811)
![{\displaystyle F(\pi ):=F[t]/\pi (t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8bc4d2be9b440370d97448e8c9b3878eea7ea2eb)
