Ricardo Baeza Rodríguez

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

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]

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

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.