Mathematics Department

Professor David Burns - publications and preprints since 2000

Edited volumes

• L-functions and Galois representations

  Proceedings of the 2004 Durham Symposium, London Math. Soc. Lecture Note Series 320, Cambridge University Press, 2007. 576 pp.

  Co-edited with K. Buzzard and J. Nekovar.

• Stark's Conjectures: Recent Work and New Directions

  Proceedings of a conference held in Baltimore in Aug. 2002, Contemp. Math. 358, American Math. Soc. (2004). 221 pp.

  Co-edited with C. Popescu, J. Sands and D. Solomon.

Research articles

• On functional equations of Euler systems

  D. Burns and T. Sano

  Submitted. Download as PDF.

• On Weil-etale cohomology and Artin L-series

  D. Burns and M. Kakde

  Submitted. Download as PDF.

• On derivatives of Kato's Euler system for elliptic curves

  D. Burns, M. Kurihara and T. Sano

  Submitted. Download as PDF.

• Hyperbolic tessellations and generators of K_3 for imaginary quadratic fields

  D. Burns, R. de Jeu, H. Gangl, A. Rahm and D. Yasaki

  Accepted to appear in Forum Math. Sigma. Download preliminary version as PDF.

• On refined conjectures of Birch and Swinnerton-Dyer type for Hasse-Weil-Artin L-series

  D. Burns and D. Macias Castillo

  Accepted to appear in Memoirs of Amer. Math. Soc. Download preliminary version as PDF.

• On Euler systems for the multiplicative group over general number fields

  D. Burns, A. Daoud, T. Sano and S. Seo

  Submitted. Download as PDF.

• On circular distributions and a conjecture of Coleman

  D. Burns and S. Seo

  Accepted to appear in Israel J. Math. Download as PDF.

• On the theory of higher rank Euler, Kolyvagin and Stark systems IV: the multiplicative group

  D. Burns, R. Sakamoto and T. Sano

  Download as PDF.

• On the theory of higher rank Euler, Kolyvagin and Stark systems III: applications

  D. Burns, R. Sakamoto and T. Sano

  Download as PDF.

• On higher special elements of p-adic representations

  D. Burns, T. Sano and K-W. Tsoi

  Accepted to appear in Int. Math. Res. Notices. Download as PDF.

• On the theory of higher rank Euler, Kolyvagin and Stark systems II: the general theory

  D. Burns, R. Sakamoto and T. Sano

  Submitted. Download as PDF.

• On a refinement of the Birch and Swinnerton-Dyer Conjecture in positive characteristic

  D. Burns, M. Kakde and W. Kim

  Submitted. Download as PDF.

• On the theory of higher rank Euler, Kolyvagin and Stark systems

  D. Burns and T. Sano

  Accepted to appear in Int. Math. Res. Notices. Download as PDF.

• On Stark elements of arbitrary weight and their p-adic families

  D. Burns, M. Kurihara and T. Sano

  Accepted to appear in Proc. Iwasawa 2017. Download as PDF.

• On non-abelian zeta elements for G_m

  D. Burns and T. Sano

  Download as PDF.

• On derivatives of p-adic L-series at s =0

  D. Burns

  2020 -- J. reine u. angew. Math. 762 53-104. Download as PDF.

• On refined metric and hermitian structures in arithmetic, I: Galois-Gauss sums and weak ramification

  W. Bley, D. Burns and C. Hahn

  2020 -- Ann. K-theory 5 79-140. Download as PDF.

• On the Galois structure of arithmetic cohomology I: compactly supported p-adic cohomology

  D. Burns

  2020 -- Nagoya Math. J. 239 294-321. Download as PDF.

• On the Galois structure of arithmetic cohomology III: Selmer groups of critical motives

  D. Burns

  2018 -- Kyoto J. Math. 58 671-693. Download as PDF.

• On the Galois structure of arithmetic cohomology II: ray class groups

  D. Burns and A. Kumon

  2018 -- J. Math. Soc. Japan 70 481-517. Download as PDF.

• On Selmer groups and refined Stark conjectures

  D. Burns and A. Livingstone Boomla

  2018 -- Bull. London Math. Soc. 50 845-862. Download as PDF.

• On Mordell-Weil groups and congruences between derivatives of twisted Hasse-Weil L-functions

  D. Burns, D. Macias Castillo and C. Wuthrich.

  2018 -- J. reine u. angew. Math. 734 187-228. Download as PDF.

• On Iwasawa theory, zeta elements for G_m and the equivariant Tamagawa number conjecture

  D. Burns, M. Kurihara and T. Sano

  2017 -- Algebra & Number Theory 11-7, 1527-1571. Download as PDF.

• On p-adic L-series, p-adic cohomology and class field theory

  D. Burns and D. Macias Castillo.

  2017 -- J. reine u. angew. Math 732 55-84. Download as PDF.

• On zeta elements for G_m

  D. Burns, M. Kurihara and T. Sano

  2016 -- Documenta Math. 21 555-626.

• On the Galois structure of Selmer groups

  D. Burns, D. Macias Castillo and C. Wuthrich.

  2015 -- Int. Math. Res. Notices 2015 11909-11933. Download as PDF.

• On main conjectures in non-commutative Iwasawa theory and related conjectures

  D. Burns

  2015 -- J. reine u. angew. Math. 698 105-160. Download as DVI file.

• Organising matrices for arithmetic complexes

  D. Burns and D. Macias Castillo

  2014 -- Int. Math. Res. Notices 2014 2814-2883. Download as PDF.

• Annihilating Selmer Modules

  J. Barrett and D. Burns

  2013 -- J. reine u. angew. Math. 675 191-222. Download as PDF.

• On Artin formalism for the conjecture of Bloch and Kato

  D. Burns

  2012 -- Math. Res. Lett. 19 1155-1169. Download as PDF.

• On special elements in higher algebraic K-theory and the Lichtenbaum-Gross Conjecture

  D. Burns, R. de Jeu and H. Gangl

  2012 -- Adv. Math. 230 1502-1529. Download as PDF.

• On main conjectures of geometric Iwasawa theory and related conjectures

  D. Burns

  No longer intended for publication (with most main results subsumed by those in the article `On Weil-etale cohomology and Artin L-series' listed above). Download as PDF.

• On derivatives of Artin L-series

  D. Burns

  2011 -- Invent. math. 186 291 -- 371. Download as PDF.

• On geometric main conjectures

  D. Burns, K. F. Lai and K-S. Tan

  2011 -- Appendix to Congruences between derivatives of geometric L-functions by D. Burns; Invent. math. 184 221--256.

• Congruences between derivatives of geometric L-functions

  D. Burns

  2011 -- Invent. math. 184 221--256. Download as PDF.

• A non-abelian Stickelberger theorem

  D. Burns and H. Johnston

  2011 -- Compositio Math. 147 35-55. Download as PDF.

• On descent theory and main conjectures in non-commutative Iwasawa theory

  D. Burns and O. Venjakob

  2011 -- J. Inst. Math. Jussieu 10 59-118. Download as DVI or as PS.

• On Equivariant Dedekind Zeta-functions at s=1

  M. Breuning and D. Burns

  2010 -- Documenta Math., Extra Volume: Andrei A. Suslin's Sixtieth Birthday, 119-146. Download as PDF.

• Leading terms and values of equivariant motivic L-functions.

  D. Burns

  2010 -- Pure App. Math. Q. 6 83-172 (John Tate Special Issue, Part II). Download as PDF.

• Algebraic p-adic L-functions in non-commutative Iwasawa theory

  D. Burns

  2009 -- Publ. RIMS Kyoto 45 75-88 (Proceedings of special semester on Arithmetic Geometry, Fall, 2006). Download as PS.

• On refined Stark conjectures in the non-abelian case

  D. Burns

  2008 -- Math. Res. Lett. 15 841-856. Download as PDF or as PS.

• Perfecting the nearly perfect.

  D. Burns

  2008 -- Pure App. Math. Q. 4 1041-1058 (Jean-Pierre Serre Special Issue, Part I). Download as DVI.

• On the Galois cohomology of ideal class groups

  D. Burns and S. Seo

  2007 -- Arch. Math. 89 536--540. Download as PS.

• Leading terms of Artin L-functions at s= 0 and s = 1.

  M. Breuning and D. Burns

  2007 -- Compositio Math. 143 1427--1464. Download as PDF.

• Congruences between derivatives of abelian L-functions at s=0.

  D. Burns

  2007 -- Invent. math. 169 451-499. Download as PDF.

• Explicit Units and the Equivariant Tamagawa Number Conjecture, II.

  D. Burns and A. Hayward

  2007 -- Comm. Math. Helv. 82 477-497. Download as DVI or Postscript.

• On the leading terms of Zeta isomorphisms and p-adic L-functions in non-commutative Iwasawa theory

  D. Burns and O. Venjakob

  2006 -- Documenta Math., Extra Volume: John H. Coates' Sixtieth Birthday, 165-209. Download as PDF.

• On the equivariant Tamagawa number conjecture for Tate motives, II

  D. Burns and M. Flach

  2006 -- Documenta Math., Extra Volume: John H. Coates' Sixtieth Birthday, 133-163. Download as PS.

• Twisted forms and relative K-theory

  A. Agboola and D. Burns

  2006 -- Proc. London Math. Soc. 92 1-28. Download as DVI or Postscript.

• Additivity of Euler characteristics in relative algebraic K-groups.

  M. Breuning and D. Burns

  2005 -- Homology, Homotopy and Applications. 7 No. 3 11-36.

• On the values of equivariant Zeta functions of curves over finite fields.

  D. Burns

  2004 -- Documenta Math. 9 357-399.

• On the refined class number formula of Gross.

  D. Burns and J. Lee

  2004 -- J. Number Theory 107 282-286.

• Refined and l-adic Euler Characteristics of nearly-perfect complexes

  D. Burns, B. Koeck and V. Snaith

  2004 -- J. Algebra 272 247-272.

• Equivariant Whitehead torsion and refined Euler characteristics

  D. Burns

  2004 -- CRM Proceedings and Lecture Notes 36 35-59.

• Equivariant Weierstrass preparation and values of L-functions at negative integers

  D. Burns and C. Greither

  2003 -- Documenta Math., Extra Volume: Kazuya Kato's Fiftieth Birthday, 157-185.

• Equivariant epsilon constants, discriminants and etale cohomology

  W. Bley and D. Burns

  2003 -- Proc. London Math. Soc. 87 545-590.

• Equivariant Tamagawa numbers and refined abelian Stark conjectures

  D. Burns

  2003 -- J. Math. Soc. Univ. Tokyo 10 225-259.

• On the equivariant Tamagawa number conjecture for Tate motives

  D. Burns and C. Greither

  2003 -- Invent. math. 153 303-359.

• Tamagawa numbers for motives with (non-commutative) coefficients II

  D. Burns and M. Flach

  2003 -- Amer. J. Math. 125 475-512.

• Etale cohomology and a generalisation of Hilbert's Theorem 132

  W. Bley and D. Burns

  2002 -- Math. Zeit. 239 1-25.

• Grothendieck groups of bundles on varieties over finite fields

  A. Agboola and D. Burns

  2001 -- K Theory 23 251-303.

• Explicit Units and the Equivariant Tamagawa Number Conjecture

  W. Bley and D. Burns

  2001 -- Amer. J. Math. 123 931-949.

• Tamagawa numbers for motives with (non-commutative) coefficients

  D. Burns and M. Flach

  2001 -- Documenta Math. 6 501-570.

• Equivariant Tamagawa Numbers, Fitting ideals and Iwasawa theory

  W. Bley and D. Burns

  2001 -- Compositio Math. 126 213-247.

• Equivariant Tamagawa Numbers and Galois module theory

  D. Burns

  2001 -- Compositio Math. 129 203-237.

• On the equivariant structure of ideals in abelian extensions of local fields (with an Appendix by W. Bley)

  D. Burns

  2000 -- Comm. Math. Helv. 75 1-44.