# Seminars (KAHW02)

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Event When Speaker Title
KAHW02 23rd March 2020
11:30 to 12:30
Federico Binda CANCELLED tba
KAHW02 23rd March 2020
14:30 to 15:30
Takeshi Saito CANCELLED Graded quotients of ramification groups of a local field with imperfect residue field
Filtration by ramification groups of the Galois group of an
extension of local fields with possibly imperfect residue fields is defined
by Abbes and the speaker. The graded quotients are abelian groups and
annihilated by the residue characteristic. We discuss the main ingredients of
the proof and the construction of injections of the character groups of the
KAHW02 23rd March 2020
16:00 to 17:00
Gunnar Carlsson CANCELLED Representation theoretic models for the algebraic K-theory of fields
Motivic cohomology provides the E_2-term of a spectral sequence converging to the algebraic K-theory of a field F.  It does not directly take into account the absolute Galois group of F.  It turns out that there is a geometric model for the algebraic K-theory of F, build out of the higher dimensional representations of its absolute Galois group.  I will discuss results, conjectures, and approaches.  This is joint work with Roy Joshua.

KAHW02 24th March 2020
10:00 to 11:00
Marc Hoyois CANCELLED Milnor excision for motivic spectra
Let k be a field and E a motivic spectrum over k which is n-torsion for some n invertible in k. We show that the cohomology theory on k-schemes defined by E satisfies Milnor excision. More generally, we give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh ∞-topos of a quasi-compact quasi-separated scheme of finite valuative dimension is hypercomplete, extending a theorem of Voevodsky to nonnoetherian schemes.

KAHW02 24th March 2020
11:30 to 12:30
Christian Haesemeyer CANCELLED On K-theories of monoids
Sets with actions by a monoid A are a non-linear analogue of categories of modules, and can be used to define various flavours of K-theory of the monoid in question. K-theory (using projective A-sets) and G-theory (using finitely generated ones) have been previously studied, but do not relate in the expected way. I will discuss joint work with Weibel clarifying why this is the case, and introducing an intermediate category of A-sets whose K-theory exhibits the behaviour analogous to that of the K-theory of finitely generates modules in the linear context

KAHW02 24th March 2020
13:30 to 14:30
Free Time
KAHW02 24th March 2020
14:30 to 15:30
Kirsten Wickelgren CANCELLED A1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
We equate various Euler classes of algebraic vector bundles, including those of Barge--Morel, Kass--W., Déglise--Jin--Khan, and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of Scheja and Storch. As an application, we compute the Euler classes associated to arithmetic counts of d-planes on complete intersections in P^n in terms of topological Euler numbers over R and C. This is joint work with Tom Bachmann

KAHW02 24th March 2020
16:00 to 17:00
Burt Totaro CANCELLED The integral Hodge conjecture for 3-folds of Kodaira dimension zero.
We prove the integral Hodge conjecture for all 3-folds X of > Kodaira dimension zero with H^0(X, K_X) not zero. > This generalizes earlier results of Voisin and Grabowski. > The assumption is sharp, in view of counterexamples by Benoist and > Ottem. We also prove similar results on the integral Tate conjecture. > For example, the integral Tate conjecture holds for abelian 3-folds in > any characteristic.

KAHW02 25th March 2020
10:00 to 11:00
Vasudevan Srinivas CANCELLED Algebraic versus topological entropy for varieties over finite fields
For an automorphism (or endomorphism) of an algebraic variety, we consider some properties of eigenvalues of the induced linear transformation on l-adic cohomology, motivated by some results from complex dynamics, related to the notion of entropy. This is a report on joint work with H'elene Esnault, and some subsequent work of K. Shuddhodan.

KAHW02 25th March 2020
11:30 to 12:30
Wiesława Nizioł CANCELLED p-adic comparison theorems for rigid analytic spaces
Classical p-adic comparison theorems link p-adic etale cohomology of schemes over local fields of mixed characteristic with their de Rham cohomology preserving all the underlying structures. I will survey the recent work on analogs of these theorems for rigid analytic varieties.
KAHW02 26th March 2020
09:00 to 10:00
Simon Pepin lehalleur CANCELLED Exponential motives and the Fourier transform
Varieties equipped with a regular function admit interesting "exponential" cohomology theories: rapid decay cohomology, twisted de Rham cohomology in characteristic 0, twisted l-adic cohomology in positive characteristic. They exhibit motivic-like properties - weights, a kind of Hodge filtration, a period isomorphism - but do not fit into the classical theory of motives. Building on ideas of Kontsevich-Soibelman and Fresán-Jossen, we construct triangulated categories of exponential Voevodsky motives equipped with functors realising exponential cohomology theories. More generally, we associate to any "six operation formalism" an exponential version. Unlike classical motivic sheaf theories, these exponential sheaf theories come with a built-in Fourier-Deligne transform, which plays a key role in the construction of exponential realisations. This is joint work in progress with Javier Fresán and Martin Gallauer.

KAHW02 26th March 2020
10:10 to 11:10
Anand Sawant CANCELLED $\mathbb A^1$-connected components of ruled surfaces
A conjecture of Morel asserts that the sheaf of $\mathbb A^1$-connected components of a space is $\mathbb A^1$-invariant.  We will discuss how the sheaves of naive" as well as `genuine" $\mathbb A^1$-connected components of a smooth projective birationally ruled surface can be determined using purely algebro-geometric methods.  We will discuss a proof of Morel's conjecture for a smooth projective surface birationally ruled over a curve of genus > 0 over an algebraically closed field of characteristic 0.  If time permits, we will indicate why the naive and genuine $\mathbb A^1$-connected components of such a birationally ruled surface do not coincide if the surface is not a minimal model and discuss some open questions and specultions regarding the situation in higher dimensions.  The talk is based on joint work with Chetan Balwe.
KAHW02 26th March 2020
11:30 to 12:30
Toni Annala CANCELLED Derived Algebraic Cobordism
The purpose of this talk is to outline how to use derived
algebraic geometry in order to give a very general geometric construction of
algebraic cobordism in the spirit of Levine and Morel. The new construction
requires no smoothness hypotheses on the variety, and works over a Noetherian
ground ring of finite Krull dimension (as opposed over a field of
characteristic 0). Moreover, the construction is naturally part of a larger
bivariant theory in the sense of Fulton and MacPherson. We will outline what
is known about derived cobordism theory. Most importantly: it has the
expected relationship with the Grothendieck ring of vector bundles and
satisfies projective bundle formula.
KAHW02 26th March 2020
14:30 to 15:30
Nikita Semenov CANCELLED Hopf-theoretic approach to motives of twisted flag varieties
Let G be a split semisimple algebraic group over a field and let A be an oriented cohomology theory in the sense of Levine-Morel. We provide a uniform approach to the A-motives of geometrically cellular smooth projective G-varieties based on the Hopf algebra structure of A(G). Using this approach we provide various applications to the structure of motives of twisted flag varieties. The talk is based on a joint work with Victor Petrov.
KAHW02 26th March 2020
16:00 to 17:00
Adeel Khan CANCELLED Chow-theoretic vs. K-theoretic Gromov-Witten invariants
Let X be a smooth projective complex variety.  We prove the comparison between the Gromov-Witten invariants of X with their K-theoretic variants defined by Givental and Lee.  The key ingredient is a virtual Grothendieck-Riemann-Roch formula on the moduli stack of stable maps, which is used to compare Kontsevich’s virtual fundamental class with the one constructed by Behrend-Fantechi.

KAHW02 27th March 2020
10:00 to 11:00
Georg Tamme CANCELLED On a conjecture of Vorst
Quillen proved that algebraic K-theory is A^1-invariant on regular noetherian schemes. Vorst’s conjecture is a partial converse. Let k be a field, and let A be a k-algebra essentially of finite type and of dimension d. Vorst’s conjecture predicts that if K_{d+1}(A) = K_{d+1}(A[t_1, \dots, t_m]) for all positive integers m, then A is regular. This conjecture was proven by Cortinas, Haesemeyer, and Weibel in case k has characteristic 0. In the talk, I will explain the proof of a slightly weaker version of the conjecture if k has positive characteristic. Joint work with Moritz Kerz and Florian Strunk.

KAHW02 27th March 2020
11:30 to 12:30
Maria Yakerson CANCELLED Motivic generalized cohomology theories from framed perspective
All motivic generalized cohomology theories acquire unique structure of so called framed transfers. If one takes framed transfers into account, it turns out that many interesting cohomology theories can be constructed simply as suspension spectra on certain moduli stacks (and their variations). This way important cohomology theories on schemes get new geometric interpretations, and so do canonical maps between different cohomology theories. In the talk we will explain the general formalism of framed transfers and show how it works for various cohomology theories. This is a summary of joint projects with Tom Bachmann, Elden Elmanto, Marc Hoyois, Joachim Jelisiejew, Adeel Khan, Denis Nardin and Vladimir Sosnilo.

KAHW02 27th March 2020
13:30 to 14:00
Free Time