STNB2026 (39a edició)
Four lectures on $p$-adic Hodge-Tate theory and applications.
Coordinació
TBA
Descripció
The classical theory of Hodge provides isomorphisms which compare the de Rham cohomology and the singular cohomology of smooth real manifolds. The p-adic version of this theory provides similar isomorphisms, which compare the étale and de Rham cohomology of smooth proper schemes over p-adic fields. This is achieved by constructing suitable comparison rings and linearization functors, which in turn have applications to the classification of p-adic representations. The contents of our series of four lectures are as follows. In the first lecture we will give an overview of the theory. In the second lecture we will discuss the case of Hodge-Tate representations, the fundamental example of Fontaine's formalism, which will guide us when we discuss more general representations in the third lecture, such as the de Rham and crystalline. In the last session, we will apply this theory to classify p-adic representations arising from elliptic curves.
Xerrades
- Overview and Motivation. (Josu Pérez Zarraonandia)
- Hodge-Tate Representations (Matilde Vieira Lino da Costa)
- Three Period Rings for the Elven-kings (Filip Gawron)
- Classification of $p$-adic Representations of Elliptic Curves ( Jose Castro-Moreno)
Referències
Olivier Brinon and Brian Conrad: CMI summer school notes on $p$-adic hodge theory, https://math.stanford.edu/~conrad/papers/notes.pdf
Abhinandan: $p$-adic Galois representations and elliptic curves, https://www.math.u-bordeaux.fr/~ybilu/algant/documents/theses/Abhinandan.pdf
