#### 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.

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

Submitted. Download as PDF.

#### On refined conjectures of Birch and Swinnerton-Dyer type for Hasse-Weil-Artin

*L*-seriesD. Burns and D. Macias Castillo

Submitted. Download 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 representationsD. 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 familiesD. Burns, M. Kurihara and T. Sano

Accepted to appear in Proc. Iwasawa 2017. 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 cohomologyD. 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*-functionsD. 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

and the equivariant Tamagawa number conjecture**G**_mD. 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 theoryD. Burns and D. Macias Castillo.

2017 -- J. reine u. angew. Math

**732**55-84. Download as PDF.#### On zeta elements for

**G**_mD. 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 ConjectureD. 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 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*-functionsD. 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 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 theoryD. Burns

2009 -- Publ. RIMS Kyoto

**45**75-88 (Proceedings of special semester on Arithmetic Geometry, Fall, 2006). Download 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 theoryD. 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 integersD. 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. Burns2003 -- J. Math. Soc. Univ. Tokyo

**10**225-259.#### On the equivariant Tamagawa number conjecture for Tate motives

D. Burns and C. Greither2003 -- Invent. math.

**153**303-359.#### Tamagawa numbers for motives with (non-commutative) coefficients II

D. Burns and M. Flach2003 -- Amer. J. Math.

**125**475-512.#### Etale cohomology and a generalisation of Hilbert's Theorem 132

W. Bley and D. Burns2002 -- Math. Zeit.

**239**1-25.#### Grothendieck groups of bundles on varieties over finite fields

A. Agboola and D. Burns2001 -- K Theory

**23**251-303.#### Explicit Units and the Equivariant Tamagawa Number Conjecture

W. Bley and D. Burns2001 -- Amer. J. Math.

**123**931-949.#### Tamagawa numbers for motives with (non-commutative) coefficients

D. Burns and M. Flach2001 -- Documenta Math.

**6**501-570.#### Equivariant Tamagawa Numbers, Fitting ideals and Iwasawa theory

W. Bley and D. Burns2001 -- Compositio Math.

**126**213-247.#### Equivariant Tamagawa Numbers and Galois module theory

D. Burns2001 -- Compositio Math.

**129**203-237.#### On the equivariant structure of ideals in abelian extensions of local fields (with an Appendix by W. Bley)

D. Burns2000 -- Comm. Math. Helv.

**75**1-44.