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# Documents  14F30 | enregistrements trouvés : 4

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## Post-edited  The category MF in the semistable case Faltings, Gerd (Auteur de la Conférence) | CIRM (Editeur )

For smooth schemes the category $MF$ (defined by Fontaine for DVR's) realises the "mysterious functor", and provides natural systems of coeffients for crystalline cohomology. We generalise it to schemes with semistable singularities. The new technical features consist mainly of different methods in commutative algebra

14F30

## Multi angle  Arithmetic $D$-modules and existence of crystalline companion Abe, Tomoyuki (Auteur de la Conférence) | CIRM (Editeur )

We will show that there exists a correspondence between smooth $l$-adic sheaves and overconvergent $F$-isocrystals over a curve preserving the Frobenius eigenvalues. Moreover, we show the existence of $l$-adic companions associated to overconvergent $F$-isocrystals for smooth varieties.
Some part of the work is done jointly with Esnault.

## Multi angle  $P$-adic cohomology of the Lubin-Tate tower Scholze, Peter (Auteur de la Conférence) | CIRM (Editeur )

We prove a finiteness result on the $p$-adic cohomology of the Lubin-Tate tower, which allows one to go from mod $p$ and $p$-adic
$GL_n (F)$-representations to Galois representations (compatibly with some global cor-respondences).

## Multi angle  The Witt vector affine Grassmannian Scholze, Peter (Auteur de la Conférence) | CIRM (Editeur )

(joint with Bhargav Bhatt) We prove that the space of $W(k)$-lattices in $W(k)[1/p]^n$, for a perfect field $k$ of characteristic $p$, has a natural structure as an ind-(perfect scheme). This improves on recent results of Zhu by constructing a natural ample line bundle on the space of such lattices.

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