Ernst Witt

Ernst Witt
Ernst Witt
	Ernst Witt inNice,1970
Born	26 June 1911; Alsen,German Empire(present-dayDenmark)
Died	3 July 1991(aged 80); Hamburg,Germany
Education	University of Göttingen
Known for	Witt algebra; Witt group; Witt's theorem; Witt vector; Bourbaki–Witt theorem; Hasse–Witt matrix; Poincaré–Birkhoff–Witt theorem
	Scientific career
Fields	Mathematics
Institutions	University of Hamburg
Doctoral advisor	Emmy Noether
Doctoral students	Walter Borho; Günter Harder; Ina Kersten;

Ernst Witt(26 June 1911 – 3 July 1991) was a Germanmathematician,one of the leadingalgebraistsof his time.^[1]

Biography

Witt was born on the island ofAlsen,then a part of theGerman Empire.Shortly after his birth, his parents moved the family toChinato work as missionaries,^[2]and he did not return to Europe until he was nine.^[2]

After his schooling, Witt went to theUniversity of Freiburgand theUniversity of Göttingen.He joined theNSDAP(Nazi Party) and was an active party member.^[3]Witt was awarded aPh.D.at the University of Göttingen in 1933 with a thesis titled: "Riemann-Roch theorem and zeta-Function in hypercomplexes"^[4](Riemann-Rochscher Satz und Zeta-Funktion im Hyperkomplexen) that was supervised byGustav Herglotz,withEmmy Noethersuggesting the topic for the doctorate.^[5]He qualified to become a lecturer and gave guest lectures in Göttingen andHamburg.^[5]He became associated with the team led byHelmut Hassewho led his habilitation. In June 1936, he gave his habilitation lecture.^[4]

DuringWorld War IIhe joined a group of five mathematicians, recruited byWilhelm Fenner,and which includedGeorg Aumann,Alexander Aigner,Oswald Teichmüller,Johann Friedrich Schultze and their leader professorWolfgang Franz,to form the backbone of the new mathematical research department in the late 1930s that would eventually be called: Section IVc ofCipher Department of the High Command of the Wehrmacht(abbr. OKW/Chi).^[6]^[7]

From 1937 until 1979, he taught at theUniversity of Hamburg.^[8]He died in Hamburg in 1991, shortly after his 80th birthday.

Work

Witt's work has been highly influential. His invention of theWitt vectorsclarifies and generalizes the structure of thep-adic numbers.^[9]It has become fundamental top-adic Hodge theory.

Witt was the founder of the theory ofquadratic formsover an arbitraryfield.^[10]He proved several of the key results, including theWitt cancellation theorem.He defined theWitt ringof all quadratic forms over a field, now a central object in the theory.^[11]

ThePoincaré–Birkhoff–Witt theoremis basic to the study ofLie algebras.Inalgebraic geometry,theHasse–Witt matrixof analgebraic curveover afinite fielddetermines the cyclicétalecoverings of degreepof a curve in characteristicp.

In the 1970s, Witt claimed that in 1940 he had discovered what would eventually be named the "Leech lattice"many years beforeJohn Leechdiscovered it in 1965, but Witt did not publish his discovery and the details of exactly what he did are unclear.^[12]^[13]

References

^Kersten, Ina(20 October 1993)."Ernst Witt 1911-1991"(PDF).Jahresbericht der Deutschen Mathematiker-Vereinigung.95:166–180.
^^a ^bSegal, Sanford L. (23 November 2014).Mathematicians under the Nazis.Princeton University Press. p. 451.ISBN 978-0-691-16463-2.
^According to Schappacher (letter in Mathematical Intelligencer 1996) it was most certainly him and notOswald Teichmüller,who attendedEmmy Noether's private seminar held in her house while wearing hisSA-uniform.
^^a ^bKersten, Ina (July 1999). "Biography of Ernst Witt (1911{1991)". In Bayer-Fluckiger, Eva; Lewis, David; Ranicki, Andrew (eds.).Quadratic Forms and Their Applications, Proceedings of the Conference on Quadratic Forms and Their Applications(PDF).University College Dublin. p. 155.
^^a ^bFrei, Günther; Lemmermeyer, Franz; Roquette, Peter J. (16 January 2014).Emil Artin and Helmut Hasse: The Correspondence 1923-1958.Contributions in Mathematical and Computational Sciences. Vol. 5. Göttingen: Springer Science & Business Media. p. 439.doi:10.1007/978-3-0348-0715-9.ISBN 978-3-0348-0715-9.
^"Army Security Agency: DF-187 The Career of Wilhelm Fenner with Special Regard to his activity in the field of Cryptography and Cryptanalysis (PDF)".Google Drive.1 December 1949. p. 7.Retrieved30 March2016.
^TICOM reports DF-187 A-G and DF-176, ‘European Axis Signal Intelligence in World War II’ vol 2
^Frei, Günther; Lemmermeyer, Franz; Roquette, Peter J. (16 January 2014).Emil Artin and Helmut Hasse: The Correspondence 1923-1958.Gottigen: Springer Science & Business Media. p. 439.ISBN 978-3-0348-0715-9.
^Rabinoff, Joseph (2014). "The Theory of Witt Vectors".arXiv:1409.7445[math.NT].
^Szymiczek, K. (8 July 2009). "Quadratic Forms". In Hazewinkel, M. (ed.).Handbook of Algebra.Vol. 6. Oxford: Elsevier. p. 70.ISBN 978-0-08-093281-1.
^Friedlander, Eric; Grayson, Daniel R. (18 July 2005).Handbook of K-Theory.Berlin: Springer Science & Business Media. pp. 539–577.ISBN 978-3-540-23019-9.
^Witt 1998,pp. 328–329.
^Edixhoven, Bas; Couveignes, Jean-Marc (20 June 2011).Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176).Princeton: Princeton University Press. p. 46.ISBN 978-0-691-14201-2.

Bibliography

Schappacher, Norbert; Scholz, Erhard (1996)."How to Write about Teichmüller".Mathematical Intelligencer.18(1): 5–6.doi:10.1007/BF03024810.S2CID 189882910.
Witt, Ernst(1998), Kersten, Ina (ed.),Collected papers. Gesammelte Abhandlungen,Berlin, New York:Springer-Verlag,ISBN 978-3-540-57061-5,MR 1643949

External links

Scholiahas a profile forErnst Witt(Q68559).

O'Connor, John J.;Robertson, Edmund F.,"Ernst Witt",MacTutor History of Mathematics Archive,University of St Andrews
Ernst Wittat theMathematics Genealogy Project

[1] Kersten, Ina(20 October 1993)."Ernst Witt 1911-1991"(PDF).Jahresbericht der Deutschen Mathematiker-Vereinigung.95:166–180.

[nine-2] Segal, Sanford L. (23 November 2014).Mathematicians under the Nazis.Princeton University Press. p. 451.ISBN 978-0-691-16463-2.

[3] According to Schappacher (letter in Mathematical Intelligencer 1996) it was most certainly him and notOswald Teichmüller,who attendedEmmy Noether's private seminar held in her house while wearing hisSA-uniform.

[habil-4] Kersten, Ina (July 1999). "Biography of Ernst Witt (1911{1991)". In Bayer-Fluckiger, Eva; Lewis, David; Ranicki, Andrew (eds.).Quadratic Forms and Their Applications, Proceedings of the Conference on Quadratic Forms and Their Applications(PDF).University College Dublin. p. 155.

[witter-5] Frei, Günther; Lemmermeyer, Franz; Roquette, Peter J. (16 January 2014).Emil Artin and Helmut Hasse: The Correspondence 1923-1958.Contributions in Mathematical and Computational Sciences. Vol. 5. Göttingen: Springer Science & Business Media. p. 439.doi:10.1007/978-3-0348-0715-9.ISBN 978-3-0348-0715-9.

[6] "Army Security Agency: DF-187 The Career of Wilhelm Fenner with Special Regard to his activity in the field of Cryptography and Cryptanalysis (PDF)".Google Drive.1 December 1949. p. 7.Retrieved30 March2016.

[7] TICOM reports DF-187 A-G and DF-176, ‘European Axis Signal Intelligence in World War II’ vol 2

[8] Frei, Günther; Lemmermeyer, Franz; Roquette, Peter J. (16 January 2014).Emil Artin and Helmut Hasse: The Correspondence 1923-1958.Gottigen: Springer Science & Business Media. p. 439.ISBN 978-3-0348-0715-9.

[9] Rabinoff, Joseph (2014). "The Theory of Witt Vectors".arXiv:1409.7445[math.NT].

[10] Szymiczek, K. (8 July 2009). "Quadratic Forms". In Hazewinkel, M. (ed.).Handbook of Algebra.Vol. 6. Oxford: Elsevier. p. 70.ISBN 978-0-08-093281-1.

[11] Friedlander, Eric; Grayson, Daniel R. (18 July 2005).Handbook of K-Theory.Berlin: Springer Science & Business Media. pp. 539–577.ISBN 978-3-540-23019-9.

[FOOTNOTEWitt1998328–329-12] Witt 1998,pp. 328–329.

[13] Edixhoven, Bas; Couveignes, Jean-Marc (20 June 2011).Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176).Princeton: Princeton University Press. p. 46.ISBN 978-0-691-14201-2.

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