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Shane Kelly

Research Assistant in
Prof. Hélène Esnault's research group
on arithmetic geometry


FB Mathematik und Informatik
Arnimallee 3, Zimmer 109
14195 Berlin
GERMANY

shane dot kelly dot uni at gmail dot com

current research interests

Arithmetic algebraic geometry (specfically motivic cohomology; motivic homotopy theory, K-theory, algebraic cycles)

Birational geometry, resolution of singularities (via differential forms in positive characteristic)

Modular representation theory (via stratified mixed Tate motives)

teaching

Winter Semester 2016/2017: Linear codes

Winter Semester 2016/2017: Étale cohomology

Summer Semester 2017: Infinity categories

Summer Semester 2017: Topological data analysis

Winter Semester 2017/2018: Number theory I

Winter Semester 2017/2018: Mathematics of Data Science

articles

(1) Voevodsky motives and ldh descent
Astérisque, 391. (2017)

(2) Mixed Motives and Geometric Representation Theory in Equal Characteristic (with Jens Niklas Eberhardt)
Submitted (2016) arXiv

(3) Un isomorphisme de Suslin
Bull. Soc. Math. Fr., accepted. (2016) arXiv

(4) Points in algebraic geometry (with Ofer Gabber)
J. Pure Appl. Algebr., Volume 219, Issue 10, pp 4667-4680 (2015) arXiv

(5) Weight homology of motives (with Shuji Saito)
Int. Math. Res. Not. (13):3938-3984. (2017). arXiv

(6) Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces (with Annette Huber)
Submitted (2017) arXiv

(7) Differential forms in positive characteristic avoiding resolution of singularities (with Annette Huber and Stefan Kebekus)
Bull. Soc. Math. Fr., accepted. (2016) arXiv

(8) The motivic Steenrod algebra in positive characteristic (with Marc Hoyois and Paul Arne Østvær)
J. Eur. Math. Soc., accepted. (2014) arXiv

(9) Vanishing of Negative K-theory in positive characteristic
Compositio Mathematica, 150, pp 1425-1434. (2014) arXiv

(10) Some observations about motivic tensor triangulated geometry over a finite field
Surveys around Ohkawa's theorem on Bousfield classes (2016) arXiv

Ph.D. thesis

Triangulated categories of motives in positive characteristic
PhD thesis cotutelle between Université de Paris-Nord 13 and Australian National University
jointly supervised by Denis-Charles Cisinski and Amnon Neeman
(2012) arXiv

undergraduate

(11) Characterizing a family of elusive groups (with Michael Giudici)
Journal of Group Theory, 12(1). (2009)

(12) Constructions of intriguing sets of polar spaces from field reduction and derivation.
Designs, Codes and Cryptography, 43(1). (2007)

(13) Tight Sets and m-Ovoids of Polar Spaces (with John Bamberg, Maska Law, and Tim Penttila)
J. Combin. Theory Ser. A, 114(7). (2007)



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