Univ.-Prof. Dr. Andreas Nickel

Univ.-Prof. Dr. Andreas Nickel

---

Research group

PostDocs

• Dr. Bence Forrás
• Dr. Katharina Müller

PhD students

• Justina Lückehe (since 2023)

Emeriti

• Prof. Dr. Cornelius Greither

Former members

• PD Dr. Sören Kleine

Former PhD students

• Dr. Bence Forrás (2020-2023): An equivariant p-adic Artin conjecture
• Dr. Antonio Mejías Gil (2018-2023): A main conjecture in non-commutative Iwasawa theory
• Dr. Nils Ellerbrock (2017-2021): Integrality of Stickelberger elements

---

Events

• Algebraic Number Theory - A workshop for young researchers (University of the Bundeswehr Munich, September 2-6, 2024)

---

Publications, theses, preprints

• S. Kleine, A. Nickel, T. Ritter, K. Shankar
  RSA+: An RSA variant,
  preprint (last update: 20th March 2024), 11 pages (pdf).
  
  
• M. Baake, Á. Bustos, A. Nickel
  On k-free numbers in cyclotomic fields: entropy, symmetries and topological invariants,
  preprint (last update: 30th November 2023), 22 pages (arXiv).
  
  
• N. Ellerbrock, A. Nickel
  Integrality of Stickelberger elements and annihilation of natural Galois modules,
  preprint (last update: 22nd March 2022), 42 pages (pdf).
  
  
• H. Johnston, A. Nickel
  An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications,
  preprint (last update: 30th November 2021), 43 pages (pdf).
  
  
• A. Nickel
  An equivariant Iwasawa main conjecture for local fields,
  preprint (last update: 10th May 2019), 38 pages (pdf).
  
  
• A. Mejías Gil, A. Nickel
  On natural complexes in Iwasawa theory,
  to appear in EMS Series of Congress Reports
  preprint (pdf).
  
  
• M. Baake, Á. Bustos, A. Nickel
  Power-free points in quadratic number fields: Stabiliser, dynamics and entropy,
  to appear in Israel J. Math.
  preprint (pdf).
  
  
• A. Nickel
  The strong Stark conjecture for totally odd characters,
  Proc. Amer. Math. Soc. 152 (2024), 147-162
  preprint (pdf).
  
  
• A. Nickel
  On the p-adic Beilinson conjecture and the equivariant Tamagawa number conjecture,
  Selecta Math. (N.S.) 28 (2022), Paper No. 3, 39pp.
  preprint (pdf).
  
  
• M. Baake, Á. Bustos, C. Huck, M. Lemańczyk, A. Nickel
  Number-theoretic positive entropy shifts with small centraliser and large normaliser,
  Ergodic Theory Dynam. Systems 41 (2021), 3201-3226
  preprint (pdf).
  
  
• A. Nickel
  Notes on noncommutative Fitting invariants,
  survey article with an appendix by H. Johnston, A. Nickel:
  Fitting invariants and Morita equivalence,
  in Development of Iwasawa theory - The Centennial of K. Iwasawa's Birth
  Adv. Stud. Pure Math. 86 (2020), 27-60
  preprint (pdf).
  
  
• H. Johnston, A. Nickel
  On the p-adic Stark conjecture at s=1 and applications,
  with an appendix by T. Hofmann, H. Johnston, A. Nickel:
  Computational verification of Leopoldt's conjecture and the Leading Term Conjectures for totally real fields,
  J. Lond. Math. Soc. 101 (2020), 1320-1354
  preprint (pdf).
  
  
• A. Nickel
  A generalization of a theorem of Swan with applications to Iwasawa theory,
  Canad. J. Math. 72 (2020), 656-675
  preprint (pdf).
  
  
• A. Nickel
  Annihilating wild kernels,
  Doc. Math. 24 (2019), 2381-2422
  preprint (pdf).
  
  
• H. Johnston, A. Nickel
  On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture,
  Math. Z. 292 (2019), 1233-1267
  preprint (pdf).
  
  
• A. Nickel
  Conjectures of Brumer, Gross and Stark,
  in Spectral Structures and Topological Methods in Mathematics (eds. M. Baake, F. Goetze, W. Hoffmann),
  EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich (2019), pp. 365-388
  preprint (pdf).
  
  
• N. Ellerbrock, A. Nickel
  On formal groups and Tate cohomology in local fields,
  Acta Arith. 182 (2018), 285-299
  preprint (pdf).
  
  
• H. Johnston, A. Nickel
  Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture,
  Amer. J. Math. 140 (2018), 245-276
  preprint (pdf).
  
  
• H. Johnston, A. Nickel
  On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results,
  Trans. Amer. Math. Soc. 368 (2016), 6539-6574
  preprint (pdf).
  
  
• A. Nickel
  Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture,
  J. Reine Angew. Math. 719 (2016), 101-132
  preprint (pdf).
  
  
• A. Nickel
  Noncommutative Fitting invariants and non-abelian Stark-type conjectures,
  habilitation thesis, University of Bielefeld (2014), 178 pages, Introduction (pdf).
  
  
• A. Nickel
  A conductor formula for completed group algebras,
  Doc. Math. 19 (2014), 601-627
  preprint (pdf).
  
  
• H. Johnston, A. Nickel
  Noncommutative Fitting invariants and improved annihilation results,
  J. Lond. Math. Soc. 88 (1), (2013), 137-160
  preprint (pdf).
  
  
• A. Nickel
  Equivariant Iwasawa theory and non-abelian Stark-type conjectures,
  Proc. Lond. Math. Soc. 106 (6), (2013), 1223-1247
  preprint (pdf).
  
  
• A. Nickel
  Leading terms of Artin L-series at negative integers and annihilation of higher K-groups,
  Math. Proc. Camb. Philos. Soc. 151 (1), (2011), 1-22
  preprint (pdf).
  
  
• A. Nickel
  On the equivariant Tamagawa number conjecture in tame CM-extensions, II,
  Compos. Math. 147 (4), (2011), 1179-1204
  preprint (pdf).
  
  
• A. Nickel
  On non-abelian Stark-type conjectures,
  Ann. Inst. Fourier 61 (6), (2011), 2577-2608
  preprint (pdf).
  
  
• A. Nickel
  On the equivariant Tamagawa number conjecture in tame CM-extensions,
  Math. Z. 268 (1), (2011) 1-35
  preprint (pdf).
  
  
• A. Nickel
  Non-commutative Fitting invariants and annihilation of class groups,
  J. Algebra 323 (10), (2010), 2756-2778
  preprint (pdf).
  
  
• A. Nickel
  The Lifted Root Number Conjecture for small sets of places,
  J. Lond. Math. Soc. 80 (2), (2009) 446-470
  preprint without proofs (pdf).
  
  
• A. Nickel
  The Lifted Root Number Conjecture for small sets of places and an application to CM-extensions,
  dissertation, University of Augsburg, 101 pages (pdf),
  published by and available at Logos Verlag Berlin (2008), also available at amazon.de.
  
  
  
  
  
  
• A. Nickel
  Ganzzahlige Galoisstrukturen und L-Reihen: II. Allgemeine Hauptordnungen in zahmen Erweiterungen,
  diploma thesis, University of Augsburg (2004), 62 pages (pdf).

---

Teaching

• WT 2024: Linear Algebra 2, Selected mathematical methods in Coding Theory and Cryptography, Higher Mathematics for Business Informatics (ILIAS/HISInOne)
• HT 2023: Linear Algebra, Algorithmic Number Theory (ILIAS/HISInOne)

---

Past Events

• p-adic Hodge theory and Iwasawa theory (Bielefeld, September 14-18, 2015)
• Stark's Conjectures, Iwasawa theory and related topics (University of Exeter, September 3-5,2018)
• School on Arithmetic Geometry on the occasion of Massimo Bertolini's 60th birthday (Essen, September 5-9, 2022)

---

Talks

• August 21, 2023, Galois Representations and Automorphic Forms, Polish Academy of Sciences Conference Center, Będlewo, Poland
  A new main conjecture in non-commutative Iwasawa theory
  
  
• May 23, 2023, Arithmetic of L-functions, ICMAT, Madrid, Spain
  A new main conjecture in non-commutative Iwasawa theory
  
  
• December 14, 2022, Oberseminar Arithmetische und Algebraische Geometrie, LMU Munich
  An unconditional proof of the abelian equivariant Iwasawa main conjecture
  
  
• December 7, 2021, Universität der Bundeswehr München
  Fitting-Invarianten und Annullation von Klassengruppen
  
  
• September 30, 2021, Mini-Workshop Algebraic Number Theory and Arithmetic, Universität der Bundeswehr München
  Some topological dynamical systems of number-theoretic origin
  
  
• June 26, 2020, RWTH Aachen (via Zoom)
  The equivariant Tamagawa number conjecture
  
  
• October 31, 2018, Number Theory and Geometry Seminar, University of Nottingham, UK
  Swan's theorem and Iwasawa theory
  
  
• June 25, 2018, Number Theory Seminar, ICMAT/Universidad Autónoma de Madrid, Spain
  Swan's theorem and Iwasawa theory
  
  
• June 5, 2018, Pure Mathematics Seminar, University of Exeter, UK
  Swan's theorem and Iwasawa theory
  
  
• March 7, 2018, GDMV 2018, Universität Paderborn
  The equivariant Tamagawa number conjecture
  
  
• July 2017, Iwasawa 2017, University of Tokyo, Japan
  Preparatory Lecture Series: Non-abelian Stark-type conjectures and noncommutative Iwasawa theory
  
  
• December 8, 2016, Bergische Universität Wuppertal
  Nicht-kommutative Fitting-Invarianten und Brumers Vermutung
  
  
• July 22, 2016, RWTH Aachen
  Noncommutative Fitting invariants and Brumer's conjecture
  
  
• July 13, 2016, Oberseminar Arithmetische und Algebraische Geometrie , LMU Munich
  The p-adic Stark conjecture and applications
  
  
• April 20, 2016, Seminarium z Arytmetycznej Geometrii Algebraicznej, Adam Mickiewicz University, Poznań, Poland
  Brumer's conjecture and generalisations
  
  
• November 27, 2015, Universität Münster
  Brumers Vermutung
  
  
• July 13, 2015, Iwasawa 2015, King's College London
  Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture
  
  
• May 21, 2015, Mathematische Gesellschaft (Colloquium), Universität Göttingen
  Stark-type conjectures
  
  
• March 23, 2015, Pure Mathematics Seminar, University of Exeter, UK
  Brumer's conjecture and generalisations
  
  
• July 10, 2014, Oberseminar Algebra, Geometrie und Zahlentheorie , Universität Duisburg-Essen
  The equivariant Tamagawa number conjecture for Tate motives
  
  
• June 26, 2014, LMU Munich
  Nicht-kommutative Fitting Invarianten und Stark-Vermutungen
  
  
• June 5, 2014, Summer school: Special values of L-functions , ENS Lyon
  Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture
  
  
• April 12, 2013, Iwasawa Theory and Galois Representations , University of Warwick, UK
  Equivariant Iwasawa theory and non-abelian Stark-type conjectures
  
  
• March 25, 2013, Number theory afternoon, Universität der Bundeswehr München
  The equivariant Tamagawa number conjecture for Tate motives and annihilation of class groups
  
  
• March 21, 2013, King's College, London
  The equivariant Tamagawa number conjecture for Tate motives and annihilation of class groups
  
  
• March 5, 2013, Applications of Iwasawa Algebras, Banff International Research Station, Banff, Alberta, Canada
  Equivariant Iwasawa theory and non-abelian Stark-type conjectures (video)
  
  
• November 23, 2012, Number Theory Seminar, Universitat Politècnica de Catalunya, Barcelona
  The equivariant Tamagawa number conjecture for Tate motives
  
  
• November 9, 2012, Seminar Representation Theory of Algebras, Universität Bielefeld
  Non-commutative Fitting invariants
  
  
• April 27, 2012, Hauptseminar Algebra und Zahlentheorie, Universität Heidelberg
  Non-abelian Stark-type conjectures
  
  
• March 10, 2012, "Hopf Algebras and Galois Module Theory"
  2012 Spring Southeastern Section Meeting of the American Mathematical Society, Tampa, Florida
  On the non-abelian Brumer-Stark conjecture (pdf)
  
  
• February 22, 2012, Universität Bielefeld
  The equivariant Tamagawa number conjecture for Tate motives
  
  
• February 15, 2012, Universität Bielefeld
  Non-commutative Fitting invariants
  
  
• October 21, 2011, Universität Bielefeld
  Non-abelian Stark-type conjectures
  
  
• July 22, 2011, Seminar München-Regensburg, LMU Munich
  Annihilation of higher K-groups
  
  
• July 13, 2011, Universität Göttingen
  Nicht-kommutative Fitting Invarianten
  
  
• March 24, 2011, Recent developments in Galois module theory,
  Centre International de Rencontres Mathématiques, Marseille-Luminy,
  Non-abelian Stark-type conjectures
  
  
• March 1, 2011, Number Theory Seminar, University of Cambridge
  Non-abelian Stark-type conjectures
  
  
• February 28, 2011, Number Theory Seminar, King's College, London
  Non-commutative Fitting invariants and the equivariant Tamagawa number conjecture
  
  
• October 28, 2010, Journées arithmétiques de Meknès, Moulay Ismail University, Meknès, Morocco
  Non-abelian Stark-type conjectures
  
  
• July 6, 2010, Iwasawa 2010, University of Toronto
  Non-commutative Fitting invariants and applications to Iwasawa theory
  
  
• June 25, 2010, AG Algebra, Universität Freiburg
  Nicht-kommutative Fitting Invarianten
  
  
• November 6, 2009, DFG-Forschergruppe "Algebraische Zykel und L-Funktionen", Universität Regensburg
  Nicht-kommutative Fitting Invarianten
  
  
• September 24, 2009, Séminaire de l'Equipe Algèbre et Théorie des Nombres, Université de Franche-Comté, Besançon,
  Non-commutative Fitting invariants and annihilation of class groups
  
  
• July 10, 2009, 26th Journées Arithmétiques , Université de Saint-Étienne
  Annihilation of ray class groups
  
  
• January 19, 2009, Séminaire théorie des nombres, Université de Limoges
  The Lifted Root Number Conjecture for small sets of places and an application to CM-extensions (pdf)
  
  
• December 5, 2008, Séminaire de Théorie des Nombres, Université Bordeaux 1
  The Lifted Root Number Conjecture for small sets of places and an application to CM-extensions (pdf)
  
  
• December 5, 2006, Oberseminar Computational Mathematics, Universität Kassel
  Über die geliftete Wurzelzahlvermutung im Falle abelscher CM-Erweiterungen
  
  
  
  

---

Last Update: 22nd March 2024