arXiv subjects

Ivan Panin

Publications and source records attributed to Ivan Panin.

At least 19 recordsLinked to original sources

arXiv2026

LLM-Guided Evolution for Medical Decision Pipelines

Adapting large language models (LLMs) to clinical workflows often requires costly fine-tuning or manual prompt and pipeline engineering. We study LLM-guided MAP-Elites evolution as an inference-time alternative for discovering medical decision strategies and provide an implementation repository at https://github.com/univanxx/llm_guided_evo_medical. We formulate urgency triage, interactive consultation, and medical image classification as evolutionary searches over executable artifacts optimized by task-specific fitness functions. Across all three settings, evolution improves over manually designed baselines under practical constraints. In triage, evolved programs increase Semigran accuracy from $77.3\%$ to $87.1\%$ and emergency recall from $0.60$ to $0.97$, while improving safety-weighted held-out MIMIC-ESI performance. In interactive consultation, evolved policies improve the accuracy--cost frontier across Llama-3, Qwen-3.5, and Gemma-4 and transfer to held-out iCRAFTMD. In PneumoniaMNIST, prompt-only evolution improves frozen MedGemma VLMs while preserving strict JSON outputs. Qualitative analysis shows that the gains come from interpretable program-level mechanisms, calibrated triage boundaries, targeted evidence acquisition, selective commitment, and finding-oriented visual decision rules, rather than superficial prompt rewording alone.

cs.CL↗

arXiv2025

Once again on an analogue of the certain Voevodsky theorem

Suppose that $F$ is an $\mathbb{A}^{1}$-invariant quasi-stable $\mathbb{Z}F_{\ast}$-presheaf. Then its Zariski sheafification $F_{Zar}$ coincides with its Nisnevich sheafification $F_{Nis}$. Moreover, if $X\in Sm/k$ is $k$-smooth, then for any $n$ there is equality $H^{n}_{Zar}(X, F_{Zar})=H^{n}_{Nis}(X,F_{Nis})$.

math.KT↗

arXiv2025

On a theorem of Harder

We prove that for any simply connected isotropic reductive group G over a Dedekind domain D, any Zariski-locally trivial principal G-bundle over D is trivial. The corresponding result for quasi-split groups was proved in 1967 by G. Harder.

math.AG↗

arXiv2023

On the Gille theorem for the relative projective line

Let $X$ be a Noetherian separated scheme. Let $G$ be a reductive $X$-group scheme, and let $E$ be a principal $G$-bundle over $\mathbb{P}^1_X$. We prove that if the restriction of $E$ to $\infty\times X$ is Zariski locally trivial, then $E$ is itself Zariski locally trivial.

math.AG↗

arXiv2023

On the Gille theorem for the relative projective line: I

We prove a relative version of a theorem on torsors on the projective line due to Philippe Gille. As a consequence we obtain a ``weak homotopy invariance'' result for torsors under reductive group schemes defined over arbitrary semi-local regular domains. Specifically, only regular semi-local domains with infinite residue fields are regarded in this preprint. However, all results of the present preprint are true (after minor modifications) for arbitrary semi-local regular domains. This will be the topic of our next preprint.

math.AG↗

arXiv2023

Pfister forms and a conjecture due to Colliot-Th\'{e}l\`{e}ne in the mixed characteristic case

let $R$ be a regular local ring of a mixed characteristic $(0,p)$ where $p\neq 2$ is a prime number. Suppose that the quotient ring $R/pR$ is also regular. Fix a non-degenerate Pfister form $Q(T_{1},\ldots,T_{2^{m}})$ over $R$ and an invertible element $c$ in $R$. Then the equation $Q(T_{1},\ldots,T_{2^{m}})=c$ has a solution over $R$ if and only if it has a solution over the fraction field $K$.

math.KT↗

arXiv2023

A presentation theorem for smooth projective schemes over discrete valuation rings

In this article, we give a proof for a geometric presentation theorem for any irreducible scheme $X$ smooth projective over a discrete valuation ring $R$. As a consequence, for any reductive $R$-group scheme $\mathbf{G}$, we prove that any generically trivial principal $\mathbf{G}$-bundle over $X$ glued to a principal $\mathbf{G}_U$-bundle over the affine line $\mathbb{A}^1_U$ for a semilocal affine scheme $U$.

math.AG↗

arXiv2023

Weak elementary fibrations

We introduce a notion of a weak elementary fibration and prove that it does exist in certain interesting cases. Our notion is a modification of the M. Artin's notion of an elementary fibration.

math.AG↗

arXiv2023

On the Grothendieck--Serre conjecture for projective smooth schemes over a DVR

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme $G$ over a regular local ring $R$ is trivial. The mixed characteristic case of the conjecture is widely open. We consider the following setup. Let $A$ be a mixed characteristic DVR, $G$ a reductive group scheme over $A$, $X$ an irreducible smooth projective $A$-scheme, $\mathcal G$ a principal $G$-bundle over $X$. Suppose $\mathcal G$ is generically trivial. We prove that in this case $\mathcal G$ is Zariski locally trivial. This result confirms the conjecture.

math.AG↗

arXiv2022

On the triangulated category of framed motives $\text{DFr}_{-}^{eff}(k)$

The category of framed correspondences $Fr_*(k)$ was invented by Voevodsky in his notes in order to give another framework for SH(k) more amenable to explicit calculations. Based on that notes and on their JAMS paper Garkusha and the author introduced in a very recent paper a triangulated category of framed bispectra $\text{SH}_{nis}^{fr}(k)$. It is shown in the latter paper that $\text{SH}_{nis}^{fr}(k)$ recovers classical Morel-Voevodsky triangulated category of bispectra $\text{SH}(k)$. For any infinite perfect field $k$ a triangulated category of $\mathbb{F}\text{r}$-motives $\text{D}\mathbb{F}\text{r}_{-}^{eff}(k)$ is constructed in the style of the Voevodsky construction of the category $\text{DM}_-^{eff}(k)$. In our approach the Voevodsky category of Nisnevich sheaves with transfers is replaced with the category of $\mathbb{F}\text{r}$-modules. To each smooth $k$-variety $X$ the $\mathbb{F}\text{r}$-motive $\text{M}_{\mathbb{F}\text{r}}(X)$ is associated in the category $\text{D}\mathbb{F}\text{r}_{-}^{eff}(k)$. We identify the triangulated category $\text{D}\mathbb{F}\text{r}_{-}^{eff}(k)$ with the full triangulated subcategory $\text{SH}^{eff}_{-}(k)$ of the classical Morel-Voevodsky triangulated category $\text{SH}^{eff}(k)$ of effective motivic bispectra. Moreover, the triangulated category $\text{D}\mathbb{F}\text{r}_{-}^{eff}(k)$ is naturally symmetric monoidal. The mentioned identification of the triangulated categories respects the symmetric monoidal structures on both sides.

math.KT↗

arXiv2022

On Grothendieck--Serre conjecture in mixed characteristic for SL_1(D)

Let R be an unramified regular local ring of mixed characteristic, D an Azumaya R-algebra, K the fraction field of R, Nrd the reduced norm homomorphism for the Azumaya R-algebra D. Let a be a unit in R. It is proved the following: suppose the equation Nrd=a has a solution over K, then it has a solution over R. Similar results are proved for regular local rings, which are geometrically regular over a discrete valuation ring of mixed characteristic. These results extend result proven by A.Sulin and the author in the middle of 90's.

math.KT↗

arXiv2022

Moving lemmas in mixed characteristic and applications

The present paper contains new geometric theorems in mixed characteristic case. We derive a bunch of cohomological consequences using these geometric theorems. Among them an isotropy result for quadratic spaces, a purity result for quadratic spaces, a result on the Grothendieck--Serre conjecture for the special linear group of an Azumaya algebra. The Gersten conjecture for the functor K2 is proved. Bloch-Ogus type result is obtained as well. Suslin's exact sequence is derived and its application to a finiteness result is given. A version of the Roitman theorem is proved.

math.KT↗

arXiv2022

On the Gersten conjecture for hermitian Witt groups

We prove that the hermitian Gersten-Witt complex is exact for Azumaya algebras with involution of the first- or second kind over a regular local ring, which is essentially smooth over a field, or over a discrete valuation ring.

math.KT↗

arXiv2021

A short exact sequence

Let R be a regular semi-local integral domain containing a field and K be its fraction field. Let mu: G --> T be an R-group schemes morphism between reductive R-group schemes, which is smooth as a scheme morphism. Suppose that T is an R-torus.Then the map T(R)/mu(G(R)) --> T(K)/mu(G(K)) is injective and certain purity theorem is true.These and other results are derived from an extended form of Grothendieck--Serre conjecture proven in the present paper for rings R as above.

math.AG↗

arXiv2019

Framed motivic $\Gamma$-spaces

We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines $\Gamma$-spaces and framed correspondences into the concept of framed motivic $\Gamma$-spaces; these are continuous or enriched functors of two variables that take values in motivic spaces and are equipped with a framing. We craft proofs of our main results by imposing further axioms on framed motivic $\Gamma$-spaces such as a Segal condition for simplicial Nisnevich sheaves, cancellation, ${\mathbb A}^{1}$- and $\sigma$-invariance, Nisnevich excision, Suslin contractibility, and grouplikeness. This adds to the discussion in the literature on coexisting points of view on the ${\mathbb A}^{1}$-homotopy theory of algebraic varieties.

math.AG↗

arXiv2018

The triangulated categories of framed bispectra and framed motives

An alternative approach to the classical Morel-Voevodsky stable motivic homotopy theory $SH(k)$ is suggested. The triangulated category of framed bispectra $SH_{nis}^{fr}(k)$ and effective framed bispectra $SH_{nis}^{fr,eff}(k)$ are introduced in the paper. Both triangulated categories only use Nisnevich local equivalences and have nothing to do with any kind of motivic equivalences. It is shown that $SH_{nis}^{fr}(k)$ and $SH_{nis}^{fr,eff}(k)$ recover the classical Morel-Voevodsky triangulated categories of bispectra $SH(k)$ and effective bispectra $SH^{eff}(k)$ respectively. We also recover $SH(k)$ and $SH^{eff}(k)$ as the triangulated category of framed motivic spectral functors $SH_{S^1}^{fr}[\mathcal Fr_0(k)]$ and the triangulated category of framed motives $\mathcal {SH}^{fr}(k)$ respectively constructed in the paper.

math.KT↗

arXiv2018

Surjectivity of the etale excision map for homotopy invariant framed presheaves

The category of framed correspondences Fr_*(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [17]. Based on the notes [17] a new approach to the classical Morel--Voevodsky motivic stable homotopy theory was developed by G.Garkusha and I.Panin in [8]. The purpose of this paper is to prove Theorem 1.1 stating that if the ground field k is infinite, then the surjectivity of the etale excision property is true for any A1-invariant stable radditive framed presheaf of Abelian groups F. The injectivity of the etale excision was proved in [9]. The surjectivity of the etale excision was proved in [9] if the ground field is infinite of characteristic not 2. In this preprint the surjectivity of the etale excision is proved in the case of any infinite ground field. As explained in the introduction to [8] all the results of [9], [1], [10] and [8] are true now automatically without any restrictions on the characteristic of the ground field.

math.KT↗

arXiv2018

Goldie ranks of primitive ideals and indexes of equivariant Azumaya algebras

Let $\mathfrak{g}$ be a semisimple Lie algebra. We establish a new relation between the Goldie rank of a primitive ideal $\mathcal{J}\subset U(\mathfrak{g})$ and the dimension of the corresponding irreducible representation $V$ of an appropriate finite W-algebra. Namely, we show that $\operatorname{Grk}(\mathcal{J}) \leqslant \dim V/d_V$, where $d_V$ is the index of a suitable equivariant Azumaya algebra on a homogeneous space. We also compute $d_V$ in representation theoretic terms.

math.RT↗