ﻻ يوجد ملخص باللغة العربية
Using topological cyclic homology, we give a refinement of Beilinsons $p$-adic Goodwillie isomorphism between relative continuous $K$-theory and cyclic homology. As a result, we generalize results of Bloch-Esnault-Kerz and Beilinson on the $p$-adic deformations of $K$-theory classes. Furthermore, we prove structural results for the Bhatt-Morrow-Scholze filtration on $TC$ and identify the graded pieces with the syntomic cohomology of Fontaine-Messing.
We develop the Hochschild analogue of the coniveau spectral sequence and the Gersten complex. Since Hochschild homology does not have devissage or A^1-invariance, this is a little different from the K-theory story. In fact, the rows of our spectral s
We formulate a conjectural p-adic analogue of Borels theorem relating regulators for higher K-groups of number fields to special values of the corresponding zeta-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresp
In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the cen
We prove that exterior powers of (skew-)symmetric bundles induce a $lambda$-ring structure on the ring $GW^0(X) oplus GW^2(X)$, when $X$ is a scheme where $2$ is invertible. Using this structure, we define stable Adams operations on Hermitian $K$-the
We define the Chow $t$-structure on the $infty$-category of motivic spectra $SH(k)$ over an arbitrary base field $k$. We identify the heart of this $t$-structure $SH(k)^{cheartsuit}$ when the exponential characteristic of $k$ is inverted. Restricting