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Ernst Witt Collected Papers Gesammelte Abhandlungen ERNST WITT COLLECTED PAPERS GESAMMELTE ABHANDLUNGEN Edited by Ina Kersten With an Essay by Günter Härder on Witt Vectors Contents Vorstellungsbericht Jahrbuch Akad. Wiss. Göttingen (1983) 100-101 Papers by Ernst Witt in Chronological Order 419 Quadratic Forms 1. Theorie der quadratischen Formen in beliebigen Körpern 2 J. reine angew. Math. 176 (1937) 31-44 Editor's Remark 16 2. Über eine Invariante quadratischer Formen mod 2 17 J. reine angew. Math. 193 (1954) 119-120 3. Über die Arfsche Invariante quadratischer Formen mod 2 (mit Wilhelm Klingenberg) 19 J. reine angew. Math. 193 (1954) 121-122 4. Verschiedene Bemerkungen zur Theorie der quadratischen Formen über einem Körper 21 Centre Beige Rech. Math., Coli. d'Algebre sup. Bruxelles 1956 (1957) 245-250 IX Contents 5. Euklidische Kongruenzsätze in metrischen Vektorräumen (mit Hanfried Lenz) 27 Unpublished 1957 Remarks by Sigrid Böge 32 6. Über quadratische Formen in Körpern 35 Unpublished 1967 Remarks by Falko Lorenz 39 7. Über die Sätze von Artin—Springer und Knebusch 41 Unpublished 1973 Class Field Theory and Function Fields Facsimile on Class Field Theory (about 1933) 42 8. Riemann—Rochscher Satz und Z-Funktion im Hyperkomplexen 43 Math. Ann. 110 (1934) 12-28 Remarks by Günter Tamme 60 9. Über ein Gegenbeispiel zum Normensatz 63 Math. Z. 39 (1935) 462-467 10. Der Existenzsatz für abelsche Funktionenkörper 69 J. reine angew. Math. 173 (1935) 43-51 11. Zur Funktionalgleichung der L-Reihen im Funktionenkörperfall 78 Unpublished 1936 Handwritten Notes Summarized by Rainer Schulze-Pillot 12. Zerlegung reeller algebraischer Funktionen in Quadrate. Schiefkörper über reellem Funktionenkörper 81 J. reine angew. Math. 171 (1934) 4-11 Remarks by Claus Scheiderer 89 13. Über die Invarianz des Geschlechts eines algebraischen Funktionenkörpers 90 J. reine angew. Math. 172 (1935) 75-76 X Contents 14. Zyklische unverzweigte Erweiterungskörper vom Primzahlgrade p über einem algebraischen Funktionenkörper der Charakteristik p (mit Helmut Hasse) 92 Monatsh. Math. Phys. 43 (1936) 477-492 15. Unverzweigte abelsche Körper vom Exponenten pn über einem algebraischen Funktionenkörper der Charakteristik p (mit Hermann Ludwig Schmid) 108 J. reine angew. Math. 176 (1937) 168-173 16. Bemerkungen zum Beweis des Hauptidealsatzes von S. Iyanaga 114 Abh. Math. Sem. Univ. Hamburg 11 (1936) 221 17. Verlagerung von Gruppen und Hauptidealsatz 115 Proc. ICM 1954, Amsterdam, Vol. II, North-Holland Publ. Comp. 1954, 71-73 Theory of Fields and Algebras 18. Algebra (a, b, 0 117 Facsimile 1934 19. Zwei Regeln über verschränkte Produkte 118 J. reine angew. Math. 173 (1935) 191-192 20. Konstruktion von galoisschen Körpern der Charakteristik p zu vorgegebener Gruppe der Ordnung pf 120 J. reine angew. Math. 174 (1936) 237-245 21. Schiefkörper über diskret bewerteten Körpern 129 J. reine angew. Math. 176 (1937) 153-156 22. p—Algebren und Pfaffsche Formen 133 Abh. Math. Sem. Univ. Hamburg 22 (1958) 308-315 Editor's Remarks 141 XI Contents Witt Vectors 23. Zyklische Körper und Algebren der Charakteristik p vom Grad pn. Struktur diskret bewerteter perfekter Körper mit vollkommenem Restklassenkörper der Charakteristik p 142 J. reine angew. Math. 176 (1937) 126-140 24. Vektorkalkül und Endomorphismen der Einspotenzreihengruppe 157 Unpublished 1969 Remark by Thomas Zink 163 Facsimile 1964 164 An Essay on Witt Vectors by Günter Härder 165 English Translation by Bärbel and Christopher Deninger Lie Theory 25. Treue Darstellung Liescher Ringe 195 J. reine angew. Math. 177 (1937) 152-160 26. Treue Darstellungen beliebiger Liescher Ringe 204 Collectanea Math. 6 (1953) 107-115 27. Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe 213 Abh. Math. Sem. Univ. Hamburg 14 (1941) 289-322 Remarks by Ulf Rehmann 247 28. Die Automorphismengruppen der Cayleyzahlen 253 J. reine angew. Math. 182 (1940) 205 29. Die Unterringe der freien Lieschen Ringe 254 Math. Z. 64 (1956) 195-216 30. Über eine Klasse von Algebren mit lauter endlich erzeugbaren Unteralgebren 276 Mitt. Math. Ges. Hamburg X (1976) 311 XII Contents Group Theory and Combinatorics 31. Über Normalteiler, deren Ordnung prim ist zum Index 277 Unpublished 1937 Editor's Remark 278 32. Die 5-fach transitiven Gruppen von Mathieu 279 Abh. Math. Sem. Univ. Hamburg 12 (1938) 256-264 33. Über Steinersche Systeme 288 Abh. Math. Sem. Univ. Hamburg 12 (1938) 265-275 An Essay on Ernst Witt's Work on the Mathieu Groups and on Steiner Systems by Peter M. Neumann 299 34. Zum Problem der 36 Offiziere 305 Jber. DMV 48 (1938) 66-67 Editor's Remark 306 35. Konstruktion endlicher Ebenen 307 Internationale Nachr., 16. Jahrgang, Nr. 72 (1962) 50-51 36. Über die Kommutatorgruppe kompakter Gruppen 308 Rend. Mat. e Appl. (5), 14 (1955) 125-129 Algebra and Number Theory 37. Eine Identität zwischen Modulformen zweiten Grades . 313 Abh. Math. Sem. Univ. Hamburg 14 (1941) 323-337 Editor's Remark 328 Facsimile 1972 329 38. Die algebraische Struktur des Gruppenringes einer endlichen Gruppe über einem Zahlkörper 330 J. reine angew. Math. 290 (1952) 231-245 Anmerkungen von Peter Roquette 345 English Abstract by Bärbel Deninger 348 39. Ein kombinatorischer Satz der Elementargeometrie 349 Math. Nachr. 6 (1952) 261-262 XIII Contents 40. Über freie Ringe und ihre Unterringe 351 Math. Z. 58 (1953) 113-114 41. Zur Theorie der Schrägverbände (mit Pascual Jordan) 353 Akad. Wiss. Lit. Mainz, Abh. math.-naturw. Kl. 1953, Nr. 5, 225-232 42. Beziehungen zwischen Klassengruppen von Zahlkörpern 361 Unpublished 1961 Facsimile 367 Editor's Remark 368 43. Über die Divergenz gewisser ^-Reihen 369 Unpublished 1969 Analysis 44. Rekursionsformel für Volumina sphärischer Polyeder .... 371 Arch. Math. 1 (1949) 317-318 45. Sobre el Teorema de Zorn 373 Rev. Mat. Hisp.-Amer. (4) 10 (1950) 82-85 46. Beweisstudien zum Satz von M. Zorn 377 Math. Nachr. 4 (1951) 434-438 47. Algunas cuestiones de matemätica intuicionista 382 Conferencias de Matemätica II, Publ. del Instituto de Matemäticas "Jorge Juan", Madrid 1951 48. Über die Konstruktion von Fundamentalbereichen 388 Ann. Mat. Pura Appl. 36 (1954) 215-221 New Proofs of Known Theorems 49. Über die Kommutativität endlicher Schiefkörper 395 Abh. Math. Sem. Univ. Hamburg 8 (1931) 413 50. Der Satz von v. Staudt—Clausen 396 Unpublished 1936 XIV Contents 51. Primzahlsatz 397 Facsimile Remarks by Horst Leptin 398 52. Ein Identitätssatz für Polynome 402 Mitt. Math. Ges. Hamburg VIII, Teil 2, (1940) 188-189 53. Über einen Satz von Ostrowski 404 Arch. Math. 3 (1952) 334 54. Über den Auswahlsatz von Blaschke 405 Abh. Math. Sem. Univ. Hamburg 19 (1955) 77 Miscellanea 55. Homöomorphie einiger Tychonoffprodukte 406 Topology and its Applications (Proc. Conf. Memorial Univ. Newfoundland, St. John's, Nfdl.,1973) 199-200. Lecture Notes in Pure and Appl. Math. 12, Dekker, New York, 1975 56. Über die Ordnungen endlicher Neokörper 408 Colloquium Talk 1977 57. Erinnerungen an Gabriel Dirac in Hamburg 410 Ann. of Discr. Math. 41 (1989) 497-498 Lists Titles of Talks 412 Book Reviews 415 Contributors to this Volume 417 Acknowledgements 418 Papers (in Chronological Order) 419 XV .
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