40 citations · 152 across the 19 of their papers we have counts for
19 papers
On pro-cdh descent on derived schemes
Shane Kelly, Shuji Saito, Georg Tamme
Grothendieck's formal functions theorem states that the coherent cohomology of a Noetherian scheme can be recovered from that of a blowup and the infinitesimal thickenings of the c…
A remark on crystalline cohomology
Moritz Kerz, Georg Tamme
We propose a new approach to crystalline cohomology based on the observation that one can lift smooth algebras uniquely "up to coherent homotopy."
On the -theory of pushouts
Markus Land, Georg Tamme
We reveal a relation between the behaviour of localizing invariants on pushouts and on pullbacks of ring spectra. More concretely, we show that the failure of sending a pus…
K-theory of non-archimedean rings II
Moritz Kerz, Shuji Saito, Georg Tamme
We study fundamental properties of analytic -theory of Tate rings such as homotopy invariance, Bass fundamental theorem, Milnor excision, and descent for admissible coverings.
Purity in chromatically localized algebraic -theory
Markus Land, Akhil Mathew, Lennart Meier +1
We prove a purity property in telescopically localized algebraic -theory of ring spectra: For , the -localization of only depends on the $T(0)\oplus \dots…
Towards Vorst's conjecture in positive characteristic
Moritz Kerz, Florian Strunk, Georg Tamme
Vorst's conjecture relates the regularity of a ring with the -homotopy invariance of its -theory. We show a variant of this conjecture in positive characteristic.
On the K-theory of pullbacks
Markus Land, Georg Tamme
To any pullback square of ring spectra we associate a new ring spectrum and use it to describe the failure of excision in algebraic -theory. The construction of this new ring sp…
K-theory of non-archimedean rings I
Moritz Kerz, Shuji Saito, Georg Tamme
We introduce a variant of homotopy K-theory for Tate rings, which we call analytic K-theory. It is homotopy invariant with respect to the analytic affine line viewed as an ind-obje…
Weak completions, bornologies and rigid cohomology
Guillermo Cortiñas, Joachim Cuntz, Ralf Meyer +1
Let be a complete discrete valuation ring with residue field of positive characteristic and with fraction field of characteristic 0. We clarify the analysis behind the…
Nonarchimedean bornologies, cyclic homology and rigid cohomology
Guillermo Cortiñas, Joachim Cuntz, Ralf Meyer +1
Let be a complete discrete valuation ring with residue field and with fraction field of characteristic 0. We clarify the analysis behind the Monsky--Washnitzer completi…
Excision in algebraic K-theory revisited
Georg Tamme
By a theorem of Suslin, a Tor-unital (not necessarily unital) ring satisfies excision in algebraic K-theory. We give a new and direct proof of Suslin's result based on an exact seq…
Algebraic K-theory and descent for blow-ups
Moritz Kerz, Florian Strunk, Georg Tamme
We prove that algebraic K-theory satisfies `pro-descent' for abstract blow-up squares of noetherian schemes. As an application we derive Weibel's conjecture on the vanishing of neg…
Towards a non-archimedean analytic analog of the Bass-Quillen conjecture
Moritz Kerz, Shuji Saito, Georg Tamme
We suggest an analog of the Bass-Quillen conjecture for smooth affinoid algebras over a complete non-archimedean field. We prove this in the rank-1 case, i.e. for the Picard group.…
The Beilinson regulator is a map of ring spectra
Ulrich Bunke, Thomas Nikolaus, Georg Tamme
We prove that the Beilinson regulator, which is a map from -theory to absolute Hodge cohomology of a smooth variety, admits a refinement to a map of -ring spectra in t…
On an analytic version of Lazard's isomorphism
Georg Tamme
We prove a comparison theorem between locally analytic group cohomology and Lie algebra cohomology for locally analytic representations of a Lie group over a nonarchimedean field o…
Multiplicative differential algebraic K-theory and applications
Ulrich Bunke, Georg Tamme
We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We…
Regulators and cycle maps in higher-dimensional differential algebraic K-theory
Ulrich Bunke, Georg Tamme
We develop differential algebraic K-theory of regular arithmetic schemes. Our approach is based on a new construction of a functorial, spectrum level Beilinson regulator using diff…
Karoubi's relative Chern character, the rigid syntomic regulator, and the Bloch-Kato exponential map
Georg Tamme
We construct a variant of Karoubi's relative Chern character for smooth, separated schemes over the ring of integers in a p-adic field and prove a comparison with the rigid syntomi…
The Relative Chern Character and Regulators
Georg Tamme
In this thesis we construct a modified version of Karoubi's relative Chern character for smooth varieties over the complex numbers or the ring of integers in a p-adic number field.…