Michael Stoll
School of Engineering and Science
Jacobs University Bremen
Campus Ring 1
28 759 Bremen, Germany

Papers, Preprints and Lecture Notes

Arithmetic Geometry |  Combinatorics |  Mathematical Biology |  Group Theory |  Galois Theory
Jacobs Course Notes |  Other Course Notes |  German Lecture Notes |  Talk Notes
arXiv | MathSciNet

Arithmetic Geometry

[AG29] Documentation for the ratpoints program (pdf, 188 kB)  arXiv
Manuscript (2008).
[AG28] with N. Bruin:
Two-cover descent on hyperelliptic curves (pdf, 310 kB)  arXiv
Preprint (2008), submitted for publication.
[AG27] Rational 6-cycles under iteration of quadratic polynomials (version 2008-06-11, pdf, 260 kB)  arXiv
Preprint (2008), submitted for publication.
MAGMA script for the computations
[AG26] Applications of the Mordell-Weil sieve (pdf, 113 kB)
Oberwolfach Report 34/2007, Oberwolfach Reports 4, no. 3, 1967-1970 (2007).
[AG25] with Y. Bugeaud, M. Mignotte, S. Siksek, and Sz. Tengely:
Integral points on hyperelliptic curves (pdf, 270 kB)  arXiv
Preprint (2008), submitted for publication.
[AG24] How to obtain global information from computations over finite fields (pdf, 23 kB)
In: Higher-dimensional geometry over finite fields, NATO Science for Peace and Security Series: Information and Communication Security 16, (D. Kaledin, Y. Tschinkel, eds.), p. 189-196, IOS Press (2008).
[AG23] with T.A. Fisher and E.F. Schaefer:
The yoga of the Cassels-Tate pairing (pdf, 209 kB)  arXiv
Preprint (2007), submitted for publication.
[AG22] with J.E. Cremona, T.A. Fisher, C. O'Neil and D. Simon:
Explicit n-descent on elliptic curves. II. Geometry (pdf, 288 kB)  arXiv
To appear in J. reine angew. Math. (accepted February 2008).
[AG21] with N. Bruin:
Deciding existence of rational points on curves: an experiment (pdf, 210 kB)  arXiv
Experiment. Math. 17, 181-189 (2008).
See also my talk in Göttingen
[AG20] with J.E. Cremona, T.A. Fisher, C. O'Neil and D. Simon:
Explicit n-descent on elliptic curves. I. Algebra (Manuscript: pdf, 350 kB)  arXiv
J. reine angew. Math. 615, 121-155 (2008)
[AG19] On the number of rational squares at fixed distance from a fifth power (Manuscript: pdf, 160 kB)  arXiv
Acta Arith. 125, 79-88 (2006)
[AG18] Finite coverings and rational points (pdf, 94 kB)
Oberwolfach Report 32/2005, Oberwolfach Reports 2, no. 3, 1824-1827 (2005).
[AG17]with B. Poonen and E.F. Schaefer:
Twists of X(7) and primitive solutions to x2 + y3 = z7 (Manuscript: pdf, 560 kB) arXiv
Duke Math. J. 137, 103-158 (2007)
[AG16] Finite descent obstructions and rational points on curves (Manuscript: pdf, 399 kB)  arXiv
Algebra & Number Theory 1, 349-391 (2007).
See also my talk at MSRI, March 30, 2006
[AG15] Independence of rational points on twists of a given curve (Manuscript: pdf, 240 kB)  arXiv
Compositio Math. 142, 1201-1214 (2006); DOI: 10.1112/S0010437X06002168, published online 25 Sep 2006
[AG14]with T. Yang:
On the L-function of the curves y2 = x5 + A (Preprint version: dvi, 66 kB  pdf, 250 kB)
J. London Math. Soc. (2) 68, 273-287 (2003)
[AG13] with J.E. Cremona:
Minimal models for 2-coverings of elliptic curves (Preprint version: pdf, 211 kB)
London Math. Soc. J. Comput. Math. 5, 220-243 (2002)
[AG12] with J.E. Cremona:
On the reduction theory of binary forms (Manuscript: pdf, 266 kB)
J. reine angew. Math. 565, 79-99 (2003)
See also my talk in Leiden, 2000 (dvi, 15 kB)
[AG11] with E.F. Schaefer:
How to do a p-descent on an elliptic curve
Trans. Amer. Math. Soc. 356, 1209-1231 (2004)
Long version:  dvi (163 kB)  pdf (360 kB)
[AG10] On the height constant for curves of genus two, II
Acta Arith. 104, 165-182 (2002)
See also my talk in Leiden, 1999 (dvi, 24 kB)
[AG9] with E.V. Flynn, F. Leprévost, E.F. Schaefer, W.A. Stein and J.L. Wetherell:
Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves
Math. Comp. 70, 1675-1697 (2001)
[AG8] Implementing 2-descent for Jacobians of hyperelliptic curves
Acta Arith. 98, 245-277 (2001)
[AG7] On the arithmetic of the curves  y2 = xl + A, II
J. Number Theory 93, 183-206 (2002).
[AG6] On the height constant for curves of genus two,
Acta Arith. 90, 183-201 (1999).
[AG5] with B. Poonen:
A local-global principle for densities
In: Scott D. Ahlgren (ed.) et al.: Topics in number theory. In honor of B. Gordon and S. Chowla.
Kluwer Academic Publishers, Dordrecht. Math. Appl., Dordr. 467, 241-244 (1999).
[AG4] with B. Poonen:
The Cassels-Tate pairing on principally polarized abelian varieties arXiv
Ann. of Math. (2) 150, 1109-1149 (1999).
[AG3] On the arithmetic of the curves  y2 = xl + A and their Jacobians
J. reine angew. Math. 501, 171-189 (1998).
[AG2] An example of a simple 2-dimensional abelian variety defined over Q with Mordell-Weil group of rank at least 20
C. R. Acad. Sci Paris 322. Série I, 849-851 (1996).
[AG1] Two simple 2-dimensional abelian varieties defined over Q with Mordell-Weil group of rank at least 19
C. R. Acad. Sci. Paris 321, Série I, 1341-1345 (1995).


[CO2] with D. Schleicher:
An introduction to Conway's games and numbers (Manuscript: pdf, 300 kB) arXiv
Moscow Mathematical Journal 6, 359-388 (2006).
[CO1] Bounds for the length of recurrence relations for convolutions of P-recursive sequences
Europ. J. Comb. 18, 707-712 (1997).

Mathematical Biology

[MB1] with E. Geigant:
Bifurcation analysis of an orientational aggregation model
J. Math. Biol. 46, 537-563 (2003)  (DOI 10.1007/s00285-002-0187-1)

Group Theory

[GR5] Some group presentations with rational growth (dvi, 29 kB)
Preprint (1995).
[GR4] Asymptotics of the growth of 2-step nilpotent groups
J. London Math. Soc. 58, 38-48 (1998).
[GR3] Rational and transcendental growth series for the higher Heisenberg groups
Invent. math. 126, 85-109 (1996).
[GR2] Asymptotics of some number theoretic functions and an application to the growth of nilpotent groups (dvi, 370 kB)
Bonner Mathematische Schriften 266 (1994) (doctoral thesis).
[GR1] Regular geodesic languages for 2-step nilpotent groups
In: A.J. Duncan, N.D. Gilbert, J. Howie (eds): Combinatorial and Geometric Group Theory, Edinburgh 1993,
Cambridge University Press, Cambridge, LMS Lecture Note Series 204, 294-299 (1995).

Galois Theory

[GA2] Construction of semiabelian Galois extensions
Glasgow Math. J. 37, 99-104 (1995).
[GA1] Galois groups over Q of some iterated polynomials
Arch. Math. 59, 239-244 (1992).

Lecture Notes of Courses Taught at Jacobs University

[JN1] Linear Algebra I (pdf, 530 kB)
Notes from Fall 2006.
[JN2] Linear Algebra II (pdf, 500 kB)
Notes from Spring 2007.
[JN3] Introductory Algebra (pdf, 530 kB)
Notes from Fall 2005.
[JN4] Introductory Number Theory (pdf, 530 kB)
Notes from Spring 2006.
[JN5] Introductory Complex Analysis (pdf, 610 kB)
Notes from Spring 2007.
[JN6] Introductory Geometry: Second Half (Algebraic Geometry) (pdf, 255 kB)
Notes from Fall 2005.
[JN7] Integration and Manifolds (pdf, 549 kB)
Notes from Fall 2007.

Link to Course Pages

Other Course Notes

[CN1] Descent on Elliptic Curves (pdf, 280 kB)  arXiv
Short Course taught at IHP in Paris, October 2004.

Lecture Notes (in German) of Courses Taught in Düsseldorf

[LN1] Abzählende Kombinatorik (pdf, 554 kB)
Vorlesungsskript vom Wintersemester 1999/2000.
[LN2] Elliptische Kurven I (pdf, 405 kB)
Vorlesungsskript vom Sommersemester 2000.
[LN3] Elliptische Kurven II (pdf, 495 kB)
Vorlesungsskript vom Wintersemester 2000/2001.
[LN4] Algebraische Kurven (pdf, 371 kB)
Vorlesungsskript vom Wintersemester 2001/2002.

Talk Notes

Rational Points on Curves of Genus 2
(Slides of a colloquium talk at the University of Warwick, 2008-01-25)  pdf (209 kB)

How to Obtain Global Information From Computations Over Finite Fields
(Slides of a talk at a Summer School in Göttingen, 2007-07-05)  pdf (90 kB)

How to Determine the Set of Rational Points on a Curve
(Slides of a talk at the MEGA 2007 Conference in Strobl, 2007-06-28)  pdf (143 kB)

How to Find the Rational Points on a Rank 1 Genus 2 Curve
(Slides of a talk at a workshop in Leiden, 2007-05-14)  pdf (170 kB)

Coverings and Mordell-Weil Sieve
(Slides of a talk at a Banff workshop, 2007-02-06)  pdf (91 kB)

Deciding Existence of Rational Points on Genus 2 Curves: A Computational Experiment
(Slides of a talk at the Clay Summer School in Göttingen, 2006-07-21)  pdf (95 kB)

Finite Descent Obstructions and Rational Points
(Slides of a talk at MSRI, 2006-03-30)  pdf (86 kB)

Finite Coverings and Rational Points
(Notes of a talk in Oberwolfach, 2005-07-19)  pdf (120 kB)

x2 + y3 = z7
(Slides of a talk in Dagstuhl, 2004-05)  pdf (118 kB)

Die Gleichung x2 + y3 = z7
(Slides (in German) of a talk in Göttingen, 2004-01-15)  pdf (89 kB)

How many rational points can a curve have?
(Slides of a talk in Bordeaux, 2001-11-23)  dvi (12 kB)

Computation of canonical heights on genus 2 Jacobians
(Slides of a talk in Bordeaux, 2001-11-22)  dvi (15 kB)

Algorithmischer Beweis kombinatorischer Identitäten
(German, Habilitationsvortrag, 1999-06-30)  dvi (34 kB)


Michael Stoll,  July 31, 2008