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Courses--Spring 2009

MATH 610 Topics in Algebra

Syllabus and general information
Homework

Selected Publications

Galoiskohomologie reeller halbeinfacher algebraischer Gruppen,
Abh. Math. Sem. Univ. Hamburg 61 (1991), 231-242
p-adic K-theory of Hecke characters of imaginary quadratic fields,
Duke Math. J. 86 (1997), 197-238
On $K_3$ of Witt vectors of length two over finite fields,
K-Theory 12 (1997), 193-226
Tate's conjecture, algebraic cycles and rational $K$-theory in characteristic p,
K-Theory 13 (1998), 109-122
Topological cyclic homology of schemes, Algebraic K-theory,
Proc. Symp. Pure Math. 67 (1999), 41-88 (with L.Hesselholt)
Applications of de Jong's theorem on alterations, Resolution of Singularities. In tribute to Oscar Zariski,
Progr. in Math. 181 (2000), 299-314
The $K$-theory of fields of characteristic p,
Invent. Math. 139 (2000), 459-493 (with M.Levine)
The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky,
J. reine angew. Math. 530 (2001), 55-103 (with M.Levine)
Motivic Cohomology over Dedekind rings,
Math. Z. 248 (2004), 773-794
Weil etale cohomology over finite fields,
Math. Ann. 330 (2004), 665-692
The cyclotomic trace map and values of zeta-functions,
Algebra and Number Theory. Proc. Silver Jubilee Conf., Univ. Hyderabad (2005), 211-225.
ArXiv page
Motivic Cohomology, K-theory and topological cyclic homology,
Handbook of K-theory, Vol. 1, Springer (2005), 193-234.
On the K-theory and topological cyclic homology of smooth schemes over a discrete valuation ring,
Trans. Amer. Math. Soc. 358 (2006), 131-145. (with L.Hesselholt)
TAMS page
The de Rham-Witt complex and p-adic vanishing cycles,
J. Amer. Math. Soc. 19 (2006), 1-36. (with L. Hesselholt)
ArXiv page JAMS page
Arithmetic Cohomology over finite fields and special values of zeta-functions,
Duke Math. J. 133 (2006), no.1, 27-58.
ArXiv page
On the K-theory of regular local $F_p$-algebras,
Topology 45 (2006), no.3, 475-493 (with L.Hesselholt)
DVI file PS file
Bi-relative algebraic K-theory and topological cyclic homology,
Invent. Math. 166 (2006), 359-395 (with L. Hesselholt).
ArXiv page
Parshin's conjecture revisited,
K-theory and Noncommutative geometry, EMS series of congress reports (2008), 413-426
ArXiv page
The affine part of the Picard scheme,
to appear in: Compositio Math.
ArXiv page
Duality via cycle complexes,
to appear in: Annals of Math.
ArXiv page
Arithmetic homology and an integral version of Kato's conjecture,
Preprint
ArXiv page
On the relative and bi-relative K-theory of rings of finite characteristic
Preprint (with L. Hesselholt)
ArXiv page
On the vanishing of negative K-groups
Preprint (with L. Hesselholt)
ArXiv page

MATH 440 Topology

Syllabus and general information