Markus Rost's Web Page

Publications and Preprints

 Publications   Preprints   Slides and Abstracts   Theses of Students 

Publications

See also the listings on the data bases of Mathematical Reviews or of Zentralblatt.

• Stabilität von gefaserten Entfaltungen mit Symmetrie, Diplomarbeit, Betreuer: Gordon Wassermann, Ruhr-Universität-Bochum, 1983. [Stability of fibered equivariant unfoldings, Diploma thesis in real singularities, Advisor: Gordon Wassermann, unpublished]

1. Regularity of line defects in 3-dimensional media, with K. Jänich, Topology 24 (1985), no. 3, 353-360. MR 815485, Zbl 588.55012.
2. Décompositions de Heegaard des extérieurs des noeuds toriques et des variétés de Seifert associées, with M. Boileau and H. Zieschang, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 18, 661-664. MR 847514, Zbl 596.57009.
3. Abbildungsdefekte in 4-Mannigfaltigkeiten (Dissertation), Regensburger Mathematische Schriften, 12, Universität Regensburg, Fachbereich Mathematik, Regensburg, 1987. MR 893817, Zbl 635.55021.
4. Meridional generators and plat presentations of torus links, with H. Zieschang, J. London Math. Soc. (2) 35 (1987), no. 3, 551-562. MR 889376, Zbl 587.57005.
5. On Heegaard decompositions of torus knot exteriors and related Seifert fibre spaces, with M. Boileau and H. Zieschang, Math. Ann. 279 (1988), no. 3, 553-581. MR 922434, Zbl 616.57008.
6. Degree four cohomological invariants for quadratic forms, with B. Jacob, Invent. Math. 96 (1989), no. 3, 551-570. MR 996554, Zbl 685.10015.
7. Durch Normengruppen definierte birationale Invarianten, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 4, 189-192. MR 1046902, Zbl 711.14004.
8. On quadratic forms isotropic over the function field of a conic, Math. Ann. 288 (1990), no. 3, 511-513. MR 1079875, Zbl 0698.12009.
9. A (mod 3) invariant for exceptional Jordan algebras, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 12, 823-827. MR 1138557, Zbl 756.17014.
10. On the Dimension of a Composition Algebra, Doc. Math. 1 (1996), 209-214. MR 1397790, Zbl 867.17004.
11. Chow Groups with Coefficients, Doc. Math. 1 (1996), 319-393. MR 1418952, Zbl 864.14002.
12. Algebras of odd degree with involution, trace forms and dihedral extensions, with D. E. Haile, M.-A. Knus, and J.-P. Tignol, Israel J. Math. 96 B (1996), 299-340. MR 1433693, Zbl 871.16017.
13. The Book of Involutions, with M.-A. Knus, A. S. Merkurjev, and J.-P. Tignol, AMS Colloquium Publications, vol. 44, American Mathematical Society, Providence, RI, 1998, 593 pp. MR 1632779, Zbl 955.16001.
14. Unramified cohomology of quadrics, I, with B. Kahn and R. Sujatha, Amer. J. Math. 120 (1998), no. 4, 841-891. MR 1637963, Zbl 913.11018.
15. The chain lemma for Kummer elements of degree 3, C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 3, 185-190. With appendix A "common slot" counterexample in degree 3 by J.-P. Tignol. MR 1674602, Zbl 934.12001.
16. A descent property for Pfister forms, J. Ramanujan Math. Soc. 14 (1999), no. 1, 55-63. MR 1700870, Zbl 1059.11033.
17. Norm Varieties and Algebraic Cobordism, Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), 77-85, Higher Ed. Press, Beijing, 2002. MR 1957022, Zbl 1042.19002.
    Errata: "Norm varieties and algebraic cobordism", Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), 649, Higher Ed. Press, Beijing, 2002. MR 1989213.
18. On the dimension and other numerical invariants of algebras and vector products, with L. Cadorin and M.-A. Knus, Algebra and Number Theory: Proceedings of the Silver Jubilee Conference University of Hyderabad/edited by Rajat Tandon. New Delhi, Hindustan Book Agency, 2005, xii, 399 p., ISBN 81-85931-57-7, MR 2193344, Zbl 1107.17001.
19. La forme trace d'une algèbre simple centrale de degré 4, with J-P. Serre and J.-P. Tignol, C. R. Acad. Sci. Paris, Ser. I 342 (2006). MR 2193651, Zbl 1110.16014.

Preprints

1986-2006 (related to the norm residue homomorphism)

• Injectivity of K₂(D) ⟶ K₂(F) for quaternion algebras (May 1986)
• On Hilbert Satz 90 for K₃ for degree-two extensions (May 1986)
• On Hilbert Satz 90 for K₃ for quadratic extensions (September 1988)
• On the spinor norm and A₀(X,K₁) for quadrics (September 1988)
• Some new results on the Chow groups of quadrics (January 1990)
• The motive of a Pfister form (January 1998)
• Chain lemma for splitting fields of symbols (August 1998)
• Notes on the Degree Formula (December 2001)
• On the basic correspondence of a splitting variety (September-November 2006)

1992-2006 (misc.)

• On the Cassels-Pfister theorem (May 1992, September 2002)
• On 14-dimensional quadratic forms, their spinors, and the difference of two octonion algebras (May 1994/March 1999)
• On vector product algebras (1996)
• Remarks on Jordan algebras (dim 9, deg 3), cubic surfaces, and del Pezzo surfaces (deg 6) (December 1996)
• Notes on invariants for quadratic forms (December 1998)
• On the Galois cohomology of Spin(14) (March 99/June 2006)
• Computations in the mod 2 Lazard ring (March 2000)
• Computation of some essential dimensions (August 2000)
• Notes on residues (July 2001)
• Essential dimension of twisted C₄ (March 2002)
• The discriminant algebra of a cubic algebra (March 2002)
• On the classification of Albert algebras (September 2002)
• A Pfister form invariant for etale algebras (September 2002)
• The multiplicative transfer for the Grothendieck-Witt ring (January 2003)
• Quadratic elements in a central simple algebra of degree four (April 2003)
• Notes on Morley's theorem (August 2003)
• Notes on cubic equations (August 2003)
• The holomorphic extension of triangle functions (February-August 2004)
• The variety of angles (March 2004)
• The metric of a (n+2)-gon in affine n-space (August 2004)
• On Kummer chains in algebras of degree 3 (January 2005)
• On Frobenius, K-theory, and characteristic numbers (March 2006)

2014

• Notes on some examples for GL₂(Z[t,1/t]) (February 2014)

2017-2019

• Cohomological invariants (mod 2) for twisted C₄ (January 2017)
• On the adjunct of an endomorphism (February 2017)
• On the discriminant of cubic polynomials (August 2018)
• On the resultant of three ternary quadratic forms (November 2018)
• On the discriminant of binary forms (November 2018)
• Notes on strict bicommutative Hopf algebras (February 2019)
• Notes on Schur functors (February 2019)
• On the orthocenter (August 2019)
• A formula for the Euler-Poncelet point (September 2019)

2022

• On a cubic identity for involutive Hopf algebras (July 2022)
• Between quadratic and symmetric bilinear forms (September 2022)

2024-2025

• Notes on the associator (April 2024/March 2025)
• Notes on associator identities (May 2024)
• Notes on free alternative algebras (June 2024)
• Notes on root systems (two roots) (September 2024)
• Notes on root systems (October 2024)

Slides and Abstracts

• On Galois Cohomology, Norm Functions and Cycles, slides for the talk at the Hermann Weyl Conference, 10-13. September 2006, Bielefeld
• Norm Residue Homomorphism, abstract for the talk at the Mathematische Arbeitstagung, Bonn, June 22-28, 2007
• The basic correspondence of a splitting variety, summary of the talk at The Abel Symposium 2007, Oslo, August 5th - 10th, 2007

Theses of Students

Mathematics Genealogy Project

Doktorarbeiten

1. Wittringhomologie, Manfred Schmid, Dissertation, Universität Regensburg, 1998.
2. On Twisted Cyclic Algebras and the Chain Equivalence of Kummer Elements, Wieland Fischer, Dissertation, Universität Regensburg, 1999.
3. The Representation Ring of the Structure Group of the Relative Frobenius Morphism [pdf], Markus Severitt, Dissertation, Universität Bielefeld, 2010. Published version: The Grothendieck ring of the structure group of the geometric Frobenius morphism, arXiv:1211.6897, MR 3240925, Zbl 1297.14052.

Diplomarbeiten

1. W-Moduln und eine axiomatische Charakterisierung der Witt-Relationen, Helga Kariopp, Diplomarbeit, Universität Regensburg, 1992.
2. Wittring-Homologie von Koniken, Anne Klingenberg, Diplomarbeit, Universität Regensburg, 1992.
3. Zur Funktorialität der Randabbildung beim Wittring und der Milnor-Scharlau-Sequenz, Achim Motscha, Diplomarbeit, Universität Regensburg, 1992.
4. Ein Modell für die Ideale Iⁿ(K) des Wittringes durch Erzeugende und Relationen, Monika Pflaum, Diplomarbeit, Universität Regensburg, 1992.
5. Vektorproduktalgebren, Susanne Maurer, Diplomarbeit, Universität Regensburg, 1998.
6. Ein tensorkategorieller Zugang zum Satz von Hurwitz, Dominik Boos, Diplomarbeit, ETH-Zürich/Universität Regensburg, 1998.
7. Zur Residuenabbildung in der Theorie quadratischer Formen, Andreas Ettner, Diplomarbeit, Universität Regensburg, 1999.
8. Motivic Homotopy Types of Projective Curves [pdf], Markus Severitt, Diplomarbeit, Universität Bielefeld, September 2006. There is also a Special Edition which is an extended version.
9. Die multiplikative quadratische Norm für den Grothendieck-Witt-Ring, Tobias Wittkop, Diplomarbeit, Universität Bielefeld, September 2006.
10. Der multiplikative Transfer auf dem Grothendieck-Witt-Ring, Simon Krsnik, Diplomarbeit, Universität Bielefeld, November 2006.
11. The S_6-symmetry of quadrangles, Svenja Glied, Diplomarbeit, Universität Bielefeld, June 2007.
12. Dreiecksfunktionen und ihre holomorphe Fortsetzung, Christian Schlüter, Diplomarbeit, Universität Bielefeld, Dezember 2007.
13. Quadratische Elemente in zentralen einfachen Algebren vom Grad vier, Katarzyna Bilas, Diplomarbeit, Universität Bielefeld, Mai 2008.
14. Normalformen und das Zentrum einer elliptischen Kurve, Fabian Sander, Diplomarbeit, Universität Bielefeld, June 2011.

Bachelor- und Masterarbeiten

The list contains merely the Bachelor theses from summer 2007.

Bielefeld, Sommersemester 2007

1. Algebren vom Grad 3 sind zyklisch, Benjamin Beine, Bachelorarbeit, Bielefeld, 2007.
2. Zyklische Algebren, Lena Büsch, Bachelorarbeit, Bielefeld, 2007.
3. Irreduzibilitätskriterien nach Selmer und Perron, Anke Demming, Bachelorarbeit, Bielefeld, 2007. [PDF-Dokument]
   Literatur:
   • Perron, Oskar, Neue Kriterien für die Irreduzibilität algebraischer Gleichungen, J. Reine Angew. Math. 132, 1907, 288-307 - MR 1580727, Zbl 38.0118.02.
   • Selmer, Ernst S., On the irreducibility of certain trinomials, Math. Scand. 4, 1956, 287-302 - journal, pdf, MR 85223, Zbl 0077.24602.
4. Die kubische Resolvente, Anna Flötotto, Bachelorarbeit, Bielefeld, 2007. [PDF-Dokument]
5. Quaternionenalgebren in allen Charakteristiken, Daniel Geukes, Bachelorarbeit, Bielefeld, 2007.
6. Über die Pfaffsche Determinante, Kristin Hohendorf, Bachelorarbeit, Bielefeld, 2007. [PDF-Dokument]
7. Über die Komposition der quadratischen Formen von beliebig vielen Variablen, Alexej Janzen, Bachelorarbeit, Bielefeld, 2007.
8. Die klassischen Invarianten für quadratische Formen, Nadeshda Janzen, Bachelorarbeit, Bielefeld, 2007.
9. Über Isotropie, hyperbolische Räume und den Satz von Witt, Christoph Oldenburg, Bachelorarbeit, Bielefeld, 2007.
10. Quadratische Reziprozität und K_2(Q), Alexander Salle, Bachelorarbeit, Bielefeld, 2007.

Hinweise zur Erstellung von Bachelor- und Diplomarbeiten

Markus Rost's Web Page