PD Dr. Fritz Hörmann


Tel:+49 176 995 203 88
eMail: m@fhoermann.org


Shimura varieties and their compactifications and integral models, arithmetic of quadratic forms, Weil representation, Borcherds' theory, Kudla's conjectures on arithmetic theta functions

Fibered (multi-)derivators, (co)homological descent, Grothendieck's six-functor-formalism, algebraic stacks

Mixed motives, periods

Rendering of fractal images: Retinamandelbrot


1 (2005)Komplexe Multiplikation,
Diploma thesis, University of Heidelberg (in German)
98 pages
2 (2010)The arithmetic volume of Shimura varieties of orthogonal type,
Ph.D. thesis, Humboldt-University of Berlin
313 pages
3 (2012)On recursive properties of certain p-adic Whittaker functions,
Journal of Number Theory 132 (2012) pp. 1438-1482
44 pages
4 (2014)The arithmetic and geometric volume of Shimura varieties of orthogonal type,
CRM Monograph Series, Vol 35, Am. Math. Soc.
151 pages
5 (2015)Fibered multiderivators and (co)homological descent,
Theory Appl. Categ., Vol. 32, 2017, No. 38, pp 1258-1362.
105 pages
6 (2016)Six Functor Formalisms and Fibered Multiderivators,
Selecta Mathematica, 24(4), pp. 2841-2925 (2018)
85 pages
7 (2017)Derivator six-functor-formalisms, Definition and Construction I55 pages
8 (2017)Derivator Six-Functor-Formalisms, habilitation thesis
(consists mainly of publications 5, 6 and 7 with an extended introduction)
231 pages
9 (2017)Enlargement of (fibered) derivators,
J. Pure Applied Algebra 224 (3), pp. 1023-1063 (2020)
40 pages
10 (2018)(j.w. M. Wendt) Derivators and Tilting,
Appendix to W. Soergel, R. Virk, M. Wendt; Equivariant motives and geometric representation theory, preprint
8 pages
11 (2020)(j.w. A. Perucca, P. Sgobba, S. Tronto) Explicit Kummer theory for quadratic fields,
JP J. Algebra, Number Theory Appl., vol. 50 (2021), no. 2, 151-178.
12 (2020)Descent for coherent sheaves along formal/open coverings,
C. R. Math. Acad. Sci. Paris 358 (2020), no. 5, 577-594.
19 pages
13 (2021)Model category structures on simplicial objects24 pages
14 (2021)Exactness of Bousfield localizations of simplicial presheaves and local lifting23 pages
15 (2021)Higher stacks as diagrams42 pages
16 (2021)A note on formal periods26 pages
17 (2022)Derivator Six-Functor-Formalisms, Construction II (revised version)105 pages
18 (2022)Six-Functor-Formalisms on Higher Stacks110 pages
19 (2023)Generalized automorphic sheaves and the proportionality principle of Hirzebruch-Mumford (revised version),
J. Inst. Math. Jussieu, First View, pp. 1 - 39
35 pages

Supervised PhD thesis

2019René RecktenwaldConstruction of six functor formalisms


Summer school Derivators, Freiburg 18.8-22.8.2014
Workshop on "Homotopical approaches to categories and geometry", Freiburg June 2-3, 2016
Workshop on Derivators, Prague, Czech Republic, December 12-16, 2016
Summer school "Degeneration of Calabi-Yau varieties and arithmetic", Freiburg, October 9-13, 2017
Workshop on Derivators, Regensburg, April 9-12, 2019

Lehrveranstaltungen vergangener Semester

Fall 2010 (McGill)Math 316 - Complex analysis
Winter 2011 (McGill)Math 571 - Higher Algebra 2
Sommer 2011 (Freiburg)Assistent Vorlesung Diskrete Algebraische Strukturen
Winter 2011/12 (Freiburg)Assistent Vorlesung Algebraische Zahlentheorie
Winter 2011/12 (Freiburg)Proseminar Elementare Zahlentheorie
Winter 2011/12 (Freiburg)Seminar on Mordell's conjecture
Sommer 2012 (Freiburg)Projektseminar Algebraische Zahlentheorie - Analysis auf Adel- und Idelgruppen
Sommer 2012 (Freiburg)Assistent Vorlesung Mathematik II für Informatiker
Sommer 2012 (Freiburg)Organisation SWAS
Winter 2012/13 (Regensburg)Lectures on Shimura varieties
Sommer 2013 (Freiburg)Proseminar Graphentheorie
Sommer 2013 (Freiburg)Assistent Vorlesung Kommutative Algebra
Winter 2013/14 (Freiburg)Seminar Algebraische Geometrie (mit Dr. M. Wendt)
Winter 2013/14 (Freiburg)Assistent Vorlesung Algebra und Zahlentheorie
Sommer 2014 (Freiburg)Vorlesung Kommutative Algebra und Einführung in die algebraische Geometrie
Winter 2014/15 (Freiburg)Seminar: Endliche Algebraische Gruppen
Winter 2014/15 (Freiburg)Assistent Vorlesung Mathematik I für Ingenieure und Informatiker
Sommer 2015 (Freiburg)Assistent Vorlesung Mathematik II für Informatiker
Winter 2015/16 (Freiburg)Lectures on Shimura varieties
Sommer 2016 (Freiburg)Vorlesung Algebraische Zahlentheorie
Sommer 2016 (Freiburg)GRK Seminar on "Codimension 2"
Winter 2016/17 (Freiburg)Seminar Klassenkörpertheorie
Sommer 2017 (Freiburg)Seminar zur Algebra
Winter 2017/18 (Freiburg)Assistent Vorlesung Mathe I für Informatiker und Ingeniuere
Sommer 2018 (Freiburg)Vorlesung Algebraische Zahlentheorie
Winter 2018/19 (Freiburg)Seminar Adele (mit Prof.Huber-Klawitter)
Winter 2018/19 (Freiburg)Assistent Vorlesung Lineare Algebra I
Sommer 2020 (Freiburg)Seminar: Abelian Varieties
Sommer 2020 (Freiburg)Proseminar: Endliche Körper

Scripts and Documents

The following are lecture notes and some writings not intended for publication. They are not always carefully proofread and sometimes preliminary.

2008Compactifications of moduli spaces and mixed Hodge structures - with applications to automorphic forms
2010The arithmetic volumes of Shimura varieties of orthogonal type
Projector slides
2011Toroidal compactifications of Hilbert modular varieties
Projector slides
2011Divisorial rings and Cox rings
2014Homotopy limits and colimits in nature - A motivation for derivators
Notes for the summer school on derivators
2014Kommutative Algebra und Einführung in die algebraische Geometrie
Vorlesungsskript (in German)
2015The Weil representation and Eisenstein series
2016The Tate and Weil conjetures for rational K3 surfaces
2016Lectures on Shimura varieties
Lecture notes
2018Algebraische Zahlentheorie
Vorlesungsskript (in German)
2018The Birch and Swinnerton-Dyer conjecture
Animated and interactive projector slides programmed in C/GLSL
2019The ∞-categorical interpretation of Abelian and non-Abelian derived functors
Preliminary notes.
2020Picard stacks and Jacobian stacks of curves
Projector slides


Familie/Family: Antonella Perucca

beamermath Animated and interactive projector slides programmed in C/GLSL

Süd-West-Arithmetik-Seminar (SWAS)

Arbeitsgruppe Zahlentheorie Freiburg/Workgroup Number Theory Freiburg

The Québec-Vermont Number Theory Seminar

First Montreal-Toronto Workshop in Number Theory

Second Montreal-Toronto Workshop in Number Theory