Ricardo Baeza Rodríguez

In this Spanish name, the first or paternal surname is Baeza.

Ricardo Baeza Rodríguez
Academic background
Alma mater	Saarland University
Academic work
Discipline	Mathematics
Sub-discipline	Number theory
Institutions	University of Talca

Ricardo Baeza Rodríguez is a Chilean mathematician who works as a professor at the University of Talca.^[1][2] He earned his Ph.D. in 1970 from Saarland University, under the joint supervision of Robert W. Berger and Manfred Knebusch.^[2][3] His research interest is in number theory.^[4]

Career

Baeza became a member of the Chilean Academy of Sciences in 1983.^[1] He was the 2009 winner of the Chilean National Prize for Exact Sciences.^[2][4] In 2012, he became one of the inaugural 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] The theorem states that if q is a nonsingular quadratic form over a field F, and ${\displaystyle \pi (t)\in F[t]}$ be a monic irreducible polynomial (with ${\displaystyle F(\pi ):=F[t]/\pi (t)}$ the corresponding field extension), then ${\displaystyle (\pi (t))\otimes q\cong q}$ if and only if ${\displaystyle q\otimes F(\pi )}$ is hyperbolic.^[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] In particular, if ${\displaystyle W_{q}(F)}$ denotes the Witt group of quadratic forms over a field F, then one can construct a group ${\displaystyle k_{n}(F)}$ and an isomorphism ${\displaystyle s_{n}:h_{n}(F)\to I^{n-1}W_{q}(F)/I^{n}W_{q}(F)}$ for every value of 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] Using this result, they deduced the characteristic two analogue of Knebusch's degree conjecture.^[8]

In 2007, Baeza and Arason found a group presentation of the groups ${\displaystyle I^{n}(K)\subset W(K)}$, generated by n-fold bilinear Pfister forms, and of the groups ${\displaystyle I^{n}W_{q}(K)\subset W_{q}(K)}$, generated by quadratic Pfister forms.^[9]

Publications

• Baeza, Ricardo (2006). Quadratic Forms Over Semilocal Rings. Springer. ISBN 9783540358169.

References

1. Member profile, Chilean Academy of Sciences, retrieved 2015-01-12.
2. "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.
3. Ricardo Baeza Rodríguez at the Mathematics Genealogy Project.
4. "Ricardo Baeza gana Premio Nacional de Ciencias Exactas", Nacion.cl, August 27, 2009.
5. List of Fellows of the American Mathematical Society, retrieved 2015-01-12.
6. 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.
7. 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.
8. 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.
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

• Official website