Ricardo Baeza Rodríguez Explained

Ricardo Baeza Rodríguez
Discipline:	Mathematics
Sub Discipline:	Number theory
Workplaces:	University of Talca
Alma Mater:	Saarland University

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

Career

Baeza became a member of the Chilean Academy of Sciences in 1983.^[3] He was the 2009 winner of the Chilean National Prize for Exact Sciences.^{[1] [4]} In 2012, he became one of the inaugural fellows of the American Mathematical Society, the only Chilean to be so honored.^{[1] [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

\pi(t)\in F[t] be a monic irreducible polynomial (with F(\pi) : = F[t]/\pi(t) the corresponding field extension), then (\pi(t)) ⊗ q\cong q if and only if q ⊗ F(\pi) is hyperbolic.

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

W _{q(F)} denotes the Witt group of quadratic forms over a field F, then one can construct a group k _{n(F)} and an isomorphism s _{n} : h _{n(F)} \to I ^{n} W ^{nW} _{q(F)} for every value of n.

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.

In 2007, Baeza and Arason found a group presentation of the groups

I ^{n(K)\subset} W(K) , generated by n-fold bilinear Pfister forms, and of the groups I ^{nW} _{q(K)\subset} W _{q(K)} , generated by quadratic Pfister forms.^[9]

Publications

• Book: Baeza, Ricardo . Quadratic Forms Over Semilocal Rings . 2006 . Springer . 9783540358169.

Notes and References

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3. http://www.academia-ciencias.cl/wp/?page_id=388 Member profile
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5. http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society
6. Baeza . Ricardo . 1990 . The norm theorem for quadratic forms over a field of characteristic 2 . Communications in Algebra . en . 18 . 5 . 1337–1348 . 10.1080/00927879008823968 . 0092-7872.
7. Aravire . Ricardo . Aravire . Roberto . 1992 . Milnor'ory and quadratic forms over fields of characteristic two . Communications in Algebra . en . 20 . 4 . 1087–1107 . 10.1080/00927879208824393 . 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 . en . 259 . 2 . 361–414 . 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 . en . 314 . 2 . 895–911 . 10.1016/j.jalgebra.2007.05.004.