nLab Victor Snaith

Victor P. Snaith is an algebraist, algebraic topologist and algebraic geometer (born 1944), prof. emeritus at Sheffield web, univ. record.

Selected writings

On algebraic cobordism and introducing Snaith's theorem:

• Algebraic cobordism and $K$-theory. Mem. Amer. Math. Soc. 21 (1979), no. 221, vii+152 pp.

• Algebraic $K$-theory and localised stable homotopy theory. Mem. Amer. Math. Soc. 43 (1983), no. 280, xi+102 pp.

• Stable homotopy around the Arf-Kervaire invariant, Progress in Mathematics 273, Birkhäuser Basel, 2009, ISBN10:3764399031

• Infinite loop maps and the complex J-homomorphism, Bull. Amer. Math. Soc. 82, 3 (1976), 508-510 MR0410741, euclid

On the J-homomorphism:

• The complex J-homomorphism. I, Proc. Lond. Math. Soc., III. Ser. 34, 269-302 (1977), (Zbl 0344.55016)

• Geometric dimension of complex vector bundles, Serie notas у simposia del Мех. Mat. Soc. 1 (1975) 199-227.

• Towards algebraic cobordism, Bull. A, M.. Soc. 83, 3 (1977).

• D. Gepner, V. Snaith, On the motivic spectra representing algebraic cobordism and algebraic K-theory, Doc. Math., 14:359–396 (electronic), 2009, pdf

Snaith’s self-description of research is as follows:

My research interests include algebraic K-theory, algebraic topology, algebraic geometry, number theory and representation theory of groups. These subjects are all closely linked together and I am inclined to use the techniques from one to solve problems in another. For example, the idea of cohomology runs through all these topics, even though cohomology and homology were first developed in the context of algebraic topology. Here is another example: stable homotopy theory is a part of algebraic topology but back in 1985/6 I used it to find a canonical, explicit form of an existence result in representation theory called Brauer’s Induction Theorem. My formula, called Explicit Brauer Induction, solved a problem posed by Brauer when he discovered his famous result in 1946.

Similarly algebraic K-theory, as developed by Quillen in 1973, is a powerful topological mathematical gadget for studying algebraic geometry which in turn is used in many of the recent advances in number theory such as Wiles’s proof of Fermat’s Last Theorem. Incidentally the application of algebraic geometry to number theory is called arithmetic-algebraic geometry.

Last revised on February 28, 2021 at 08:41:50. See the history of this page for a list of all contributions to it.