Markus Rost's Web Page
Publications and Preprints
Publications Preprints Slides and Abstracts Theses of Students
See also the listings on the data bases of
Mathematical
Reviews or of
Zentralblatt.
- Regularity of line defects in
3-dimensional media, with K. Jänich, Topology 24 (1985),
no. 3, 353-360. MR 0815485,
Zbl 588.55012.
- 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 0847514,
Zbl 596.57009.
- Abbildungsdefekte in
4-Mannigfaltigkeiten, Regensburger Mathematische Schriften, 12,
Universität Regensburg, Fachbereich Mathematik, Regensburg,
1987. MR 0893817,
Zbl 635.55021.
- Meridional generators and plat
presentations of torus links, with H. Zieschang, J. London
Math. Soc. (2) 35 (1987), no. 3, 551-562.
MR 0889376,
Zbl 587.57005. ·
Link
to Journal.
- 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 0922434,
Zbl 616.57008.
- Degree four cohomological invariants for quadratic
forms, with B. Jacob, Invent. Math. 96 (1989), no. 3, 551-570.
MR 0996554,
Zbl 685.10015.
- Durch Normengruppen
definierte birationale Invarianten, C. R. Acad. Sci. Paris
Sér. I Math. 310 (1990), no. 4, 189-192.
MR 1046902,
Zbl 711.14004.
- On quadratic forms
isotropic over the function field of a conic, Math. Ann. 288
(1990), no. 3, 511-513. MR 1079875,
Zbl 706.11065.
- 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.
- On
the Dimension of a Composition Algebra, Doc. Math. 1 (1996),
209-214. MR 1397790,
Zbl 867.17004.
- Chow
Groups with Coefficients, Doc. Math. 1 (1996), 319-393.
MR 1418952,
Zbl 864.14002.
- 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.
- 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.
- 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.
- 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.
- A descent property
for Pfister forms, J. Ramanujan Math. Soc. 14 (1999), no. 1,
55-63. MR 1700870,
Zbl 1059.11033.
- 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.
- 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.
- 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.
- Injectivity of
K2(D) -> K2(F) for quaternion algebras
(May 86)
- On Hilbert Satz 90 for
K3 for degree-two extensions (May 86)
- On Hilbert Satz 90 for
K3 for quadratic extensions (September 88)
- On the spinor norm and
A0(X,K1) for quadrics (September 88)
- Some new results on the
Chow groups of quadrics (January 90)
- On 14-dimensional
quadratic forms, their spinors, and the difference of two octonion
algebras (May 94)
- The motive of a Pfister
form (January 98)
- Chain lemma for
splitting fields of symbols (August 98)
- Computations in the mod 2
Lazard ring (March 2000)
- Computation of some essential
dimensions (August 2000)
- Notes on the
Degree Formula (December 2001)
- Essential dimension of twisted
C4 (March 2002)
- The discriminant algebra of a
cubic algebra (March 2002)
- On the Cassels-Pfister theorem
(May 1992, September 2002)
- On the classification of Albert
algebras (September 2002)
- Notes on invariants
for quadratic forms (December 1998)
- 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)
- Remarks on Jordan algebras (dim 9,
deg 3), cubic surfaces, and del Pezzo surfaces (deg 6) (December
1996)
- 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)
- On vector product algebras
(1996)
- Notes on residues
(July 2001)
- The metric of a (n+2)-gon in
affine n-space (August 2004)
- On Kummer
chains in algebras of degree 3 (Notes 2005)
- On Frobenius, K-theory, and
characteristic numbers (March 2006)
- On the Galois
cohomology of Spin(14) (March 99/June 2006)
- On the basic
correspondence of a splitting variety (September-November 2006)
- Notes on some
examples for GL2(Z[t,1/t]) (February 2014)
- 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)
- On a cubic identity for
involutive Hopf algebras (July 2022)
- Between quadratic and symmetric
bilinear forms (September 2022)
- 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
Doktorarbeiten
- Wittringhomologie,
Manfred Schmid, Dissertation, Universität Regensburg,
1998.
- On Twisted Cyclic Algebras
and the Chain Equivalence of Kummer Elements, Wieland Fischer,
Dissertation, Universität Regensburg, 1999.
- The Representation Ring of the Structure
Group of the Relative Frobenius
Morphism [pdf], Markus
Severitt, Dissertation, Universität Bielefeld,
2010. Published version: MR 3240925,
Zbl 1297.14052.
Diplomarbeiten
- W-Moduln und eine axiomatische
Charakterisierung der Witt-Relationen, Helga Kariopp,
Diplomarbeit, Universität Regensburg, 1992.
- Wittring-Homologie von Koniken, Anne
Klingenberg, Diplomarbeit, Universität Regensburg, 1992.
- Zur Funktorialität der Randabbildung beim
Wittring und der Milnor-Scharlau-Sequenz, Achim Motscha,
Diplomarbeit, Universität Regensburg, 1992.
- Ein Modell für die Ideale In(K)
des Wittringes durch Erzeugende und Relationen, Monika Pflaum,
Diplomarbeit, Universität Regensburg, 1992.
- Vektorproduktalgebren, Susanne
Maurer, Diplomarbeit, Universität Regensburg, 1998.
- Ein tensorkategorieller
Zugang zum Satz von Hurwitz, Dominik Boos, Diplomarbeit,
ETH-Zürich/Universität Regensburg, 1998.
- Zur Residuenabbildung in der Theorie
quadratischer Formen, Andreas Ettner, Diplomarbeit,
Universität Regensburg, 1999.
- Motivic Homotopy Types of Projective
Curves, Markus Severitt,
Diplomarbeit, Universität Bielefeld, September 2006.
- Die
multiplikative quadratische Norm für den
Grothendieck-Witt-Ring, Tobias Wittkop, Diplomarbeit,
Universität Bielefeld, September 2006.
- Der
multiplikative Transfer auf dem Grothendieck-Witt-Ring, Simon
Krsnik, Diplomarbeit, Universität Bielefeld, November 2006.
- The S_6-symmetry of
quadrangles, Svenja Glied, Diplomarbeit, Universität
Bielefeld, June 2007.
- Dreiecksfunktionen und ihre holomorphe Fortsetzung, Christian
Schlüter, Diplomarbeit, Universität Bielefeld, Dezember
2007.
- Quadratische Elemente in zentralen einfachen Algebren vom Grad
vier, Katarzyna Bilas, Diplomarbeit, Universität Bielefeld,
Mai 2008.
- Normalformen und das
Zentrum einer elliptischen Kurve, Fabian Sander,
Diplomarbeit, Universität Bielefeld, June 2011.
Bachelorarbeiten
Die folgende Liste ist hochgradig unvollständig!
Bielefeld, Sommersemester 2007
- Algebren vom Grad 3 sind zyklisch, Benjamin Beine,
Bachelorarbeit, Bielefeld, 2007.
- Zyklische Algebren, Lena Büsch,
Bachelorarbeit, Bielefeld, 2007.
- 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 - Zbl 38.0118.02.
- Selmer,
Ernst S., On the irreducibility of certain trinomials,
Math. Scand. 4, 1956, 287-302 -
journal,
pdf,
MR 0085223,
Zbl 0077.24602.
- Die kubische Resolvente, Anna Flötotto, Bachelorarbeit,
Bielefeld, 2007. [PDF-Dokument]
- Quaternionenalgebren in allen Charakteristiken, Daniel Geukes,
Bachelorarbeit, Bielefeld, 2007.
- Über die Pfaffsche Determinante, Kristin Hohendorf,
Bachelorarbeit, Bielefeld, 2007.
[PDF-Dokument]
- Über die Komposition der quadratischen Formen von beliebig
vielen Variablen, Alexej Janzen, Bachelorarbeit, Bielefeld,
2007.
- Die klassischen Invarianten für quadratische Formen,
Nadeshda Janzen, Bachelorarbeit, Bielefeld, 2007.
- Über Isotropie, hyperbolische Räume und den Satz von
Witt, Christoph Oldenburg, Bachelorarbeit, Bielefeld, 2007.
- Quadratische Reziprozität und K_2(Q), Alexander Salle,
Bachelorarbeit, Bielefeld, 2007.
Markus Rost's Web Page