Find the fish (Autumn 2002)

Research

My research interests are Euler systems and the interplay between p-adic Hodge theory and Iwasawa theory. Here are the notes of a talk about my recent joint work on Euler systems with Guido Kings, Antonio Lei and David Loeffler. Here are the notes from my talk at the Harris conference, which contain some new ideas about the theory of Euler systems.

Preprints

Euler systems for GSp(4)
(joint with D. Loeffler and C. Skinner) preprint (pdf)
Syntomic regulators of Asai--Flach classes
(joint with D. Loeffler and C. Skinner) preprint (pdf)
Euler systems for Hilbert modular surfaces
(joint with A. Lei and D. Loeffler) preprint (pdf)
Rankin-Eisenstein classes for modular forms
(joint with G. Kings and D. Loeffler) submitted (pdf)

To appear

Rankin-Eisenstein classes and explicit reciprocity laws
(joint with G. Kings and D. Loeffler) to appear in Cambridge Journal of Math. (pdf)
Iwasawa theory for the symmetric square of a modular form
(joint with D. Loeffler) to appear in J. Reine Angew. Math (pdf)
On the asymptotic growth of Bloch-Kato-Shafarevich-Tate groups of modular forms over cyclotomic extensions
(joint with A. Lei and D. Loeffler) to appear in Canadian Jour. Math. (pdf)
Rankin--Eisenstein classes in Coleman families
(joint with D. Loeffler) to appear in Res. Math. Sci. (Robert Coleman memorial volume) (pdf)

Publications

Finite polynomial cohomology for general varieties
(joint with A. Besser and D. Loeffler) P-adic Variation in Number Theory (Glenn Stevens' 60th birthday), Annales mathématiques du Québec 40 (2016), no. 1, 203—220 (pdf)
Euler systems for modular forms over imaginary quadratic fields
(joint with A. Lei and D. Loeffler) Compositio Mathematica 151 (2015), no. 9, 1585—1625 (pdf)
Iwasawa theory and p-adic L-functions over Zp^2-extensions
(joint with D. Loeffler) International Journal of Number Theory 10 (2014), no. 8, 2045—2095 (pdf)
Local epsilon isomorphisms
(joint with D. Loeffler and O. Venjakob) Kyoto Journal of Mathematics 55 (2015), no. 1, 63—127 (pdf)
Euler systems for Rankin-Selberg convolutions
(joint with A. Lei and D. Loeffler) Annals of Math. 180 (2014), no. 2, 653—771 (pdf)
Critical slope p-adic L-functions for CM modular forms
(joint with A. Lei and D. Loeffler) Israel Journal of Math. 198 (2013), no. 1, 261—282 (pdf)
Signed Selmer groups over p-adic Lie extensions
(joint with A. Lei) Jour. Théorie de Nombres de Bordeaux, 24 (2012), no. 2, p. 377—403 (pdf)
Wach modules and critical slope p-adic L-functions
(joint with D. Loeffler) J. Reine Angew. Math., 679 (2013), p. 181—206 (pdf)
Bloch-Kato exponential maps for local fields with imperfect residue fields
Proc. London Math. Soc., 103 (2011), no. 6, p. 1007—1048 (pdf)
Coleman maps and the p-adic regulator
(joint with A. Lei and D. Loeffler) Algebra & Number Theory, 5 (2011), no. 8, p. 1095—1131 (pdf)
Akashi series of Selmer groups
Math. Proc. Camb. Phil. Soc., 151 (2011), no. 2, p. 229—243 (pdf)
Wach modules and Iwasawa theory for modular forms
(joint with A. Lei and D. Loeffler) Asian Journal of Mathematics 14 (2010), no. 4, p. 475—528 (pdf)
Generalized Euler characteristics of Selmer groups
Proc. London Math. Soc. 98 (2009), no. 3, p. 775—796 (pdf)
Euler characteristics of Selmer groups I
J. London Math. Soc. 70 (2004), no. 3, p. 586—608. (pdf)

My Erdős number is 5, via the path Erdős—Vaughan—Velani—Hill—Loeffler—Zerbes.

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